Radiometric dating such as radiocarbon dating is commonly used for measuring the age of rocks, including meteorites. This is normally an active in-situ measurement. But spectral differences between isotopes can also be used to measure isotope ratios remotely. That's how we can measure the deuterium-to-hydrogen ratio in the solar system. In principle, is it possible to measure the radioactive isotope ratio remotely? How feasible is this and how far are we from having the technology to do this?
I agree with @Heopps answer: No.
But there are a few more details.
We can measure the D/H ratio in the solar system because much of the hydrogen is in molecules that are gases: water, methane, ammonia, H2, etc. Gaseous species have spectra consisting of very narrow emission and absorption lines (also here) at very accurately known frequencies/wavelengths. For species like deuterated water, HDO, those line frequencies are significantly different from those of "normal" water, H2O.
If you can get enough light from an object with emitting or absorbing gases to get a high-resolution spectrum, you can identify the lines and which molecules are causing them, and get an estimate of how much is there. Getting the relative abundances of HDO and H2O, or CH3D and CH4, etc., lets you calculate the D/H ratio.
Unfortunately, neither 'Oumuamua nor BZ is producing enough gas to get any kind of gas spectrum, much less a high-resolution spectrum. If the estimates of how long BZ has been in its orbit are anywhere close it probably exhausted its gas long ago, even orbiting at 5 AU. And the only way we know 'Oumuamua is a comet is that the feeble amounts of gas it produced made a tiny change in its velocity and thus its hyperbolic orbit. Astronomers had been looking for evidence of comet-like activity (like having a faint coma) but saw nothing. So we'll get no D/H ratio measurement from either unless we go there and find some H-containing molecules there that haven't evaporated. That will be really difficult for 'Oumuamua!
Concerning radiometric dating, the only radioisotopes with half-lives applicable for deep time age measurements are bound up in solids ('minerals'). The measurable spectra of solids are nothing like the nice, orderly line spectra of gases. It is extremely difficult to identify a single particular solid species from a spectrum. In gas spectra the lines can cause the light intensity received by a spectrometer to change by orders of magnitude with just a tiny change in wavelength. This makes them so easy to identify, since for a given gas species the wavelengths where this happens are very well known.
But spectra of solids are very broad and change very slowly with changing wavelength, so identifying even a pure substance from its spectrum can be difficult. In an astronomical object you don't have a pure substance, you have a mix of many different minerals. The spectrum you measure is the sum of many different minerals' spectra—good luck sorting that out! As @Heopps said, the only practical ways to measure radioisotope relative abundances are with samples in hand, either by mass spectrometry or neutron activation analysis (which is rarely used anymore).
Thus trying to measure remotely the relative abundances of trace radioisotopes like uranium and lead, or rubidium and strontium, is hopeless. Which is a shame: planetary scientists, astrophysicists, cosmologists, all have several avenues of investigation they would love to pursue, if only they could get age measurements for things we can't access yet except through the telescopes.
EDIT 2018 July 15
@Heopps edit to their answer suggests a very small wavelength shift between "normal" and deuterated hydrogen-bearing species, and the source they cite indeed says it should be a factor of 1/3672 (0.027%). But I checked a summary of measured normal and deuterated water vibrational lines and their differences are huge: for the $\nu1$, $\nu2$, and $\nu3$ vibrational modes of normal water the wavelengths are 2.73441 $\mu$m, 6.27077 $\mu$m, and 2.66248 $\mu$m, respectively, while for HDO they are 3.69099 $\mu$m, 7.16178 $\mu$m, and 2.70541 $\mu$m, respectively. (I did the conversion from wavenumber to wavelength) This ranges from 1.6% for the $\nu3$ mode up to 35% for the $\nu1$ mode!
The summary source cited references given at the bottom of this post. That journal is certainly the right place to go.
These big differences are consistent with my experience doing radio astronomy at the Caltech Submillimeter Observatory at Mauna Kea, Hawaii. When we measured lines from both "normal" species and their deuterated counterparts, the differences in frequencies were so large we had to completely retune the receivers' reference oscillators; you couldn't even come close to fitting both normal and deuterated lines in one receiver bandwidth.
I wonder what we're missing in that University of Köln class lecture presentation. I admit I only skimmed it, so I might have missed an important point buried in there. Any comments from spectroscopists out there?
J. Tennyson, P. F. Bernath, L. R. Brown, A. Campargue, A. G. Császár, L. Daumont, R. R. Gamache, J. T. Hodges, O. V. Naumenko, O. L. Polyansky, L. S. Rothman, R. A. Toth, A. C. Vandaele, N. F. Zobov, S. Fally, A. Z. Fazliev, T. Furtenbacher, I. E. Gordon, S.-M. Hu, S. N. Mikhailenko and B. A. Voronin, Critica evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD16O, HD17O, and HD18O. Journal of Quant. Spectrosc. Radiat. Transfer 111 (2010) 2160-2184.
J. Tennyson, P. F. Bernath, L. R. Brown, A. Campargue, A. G. Császár, L. Daumont, R. R. Gamache, J. T. Hodges, O. V. Naumenko, O. L. Polyansky, L. S. Rothman, A. C. Vandaele, N. F. Zobov, A. R. Al Derzia, C. Fábri, A. Z. Fazliev, T. Furtenbacher, I. E. Gordon, L. Lodi and I. Mizus, IUPAC critical evaluation of the rotational-vibrational spectra of water vapor, Part III: Energy levels and transition wavenumbers for H216O, Journal of Quant. Spectrosc. Radiat. Transfer 117 (2013) 29-58.
After some research:
I found this about the measurements of hydrogen/deuterium ratio is Solar System.
Yes, different isotopes have some differences in optical spectra. For your example deuterium nuclei is twice heavier than hydrogen. Here is a study of the effect. At page 14 stated that deuterium spectral lines have 1/3672(=0.027%) more short wavelength than hydrogen.
For other nuclei the ratio is less. But also hydrogen is one of main constituents of comet as part of water, so it should be very prominent in optical spectra. For other nuclei, such as uranium/lead, it's not the case. So, the specra of the elements will be swamped in lines of more abundant elements.
Also we should not forget that the targets like `Oumuamua are very dim for high-resolution spectroscopy even with largest existing telescopes.
So - mathematically it's possible (if the target has ejecta), but physically impossible, I think.
As @Tom Spilker said in his answer, we need single-atom spectra, not solid-state spectra.
Let's imagine an ideal situation. `Oumuamua is impacted by another asteroid. For a short time a part of the ejecta is ionized, so we can see single-atom spectra of the all constituent atoms.
Let's imagine also we have an ideal Big Fantastic Telescope (BFT) with the mirror size of several kilometers. So we have enough sensitivity to captrure the impact and obtain high-resolution spectra.
Even than we'll have one more problem - Doppler broadening of spectral lines. Some of the ejecta atoms will have velocities "to us", others in opposite direction, so there are some different frequencies of the spectral lines. The spectral lines become broad, and most probably impossible to resolve tiny differences caused by isotopes.
Ergo, even "mathematically" it's doubtful, unfortunatelly.
P.S. One of my favorite phrases: "It makes our real achievements even more exciting!"