Your explosion would be limited to either above the chromosphere, or approximately on the surface using a leading ballistic plow to get further penetration, like what bunker buster bombs do. Either the leading plow, or the bomb itself would necessarily have to have an ablative sphere, because that region has an extremely low-density gas. It's not so important that there's a low-density, but the product of density times you speed.
It's reasonable to imagine a dive-bomb initiated from the outer solar system, like around Jupiter. Using gravitational assist it's not unreasonable to kill your orbital momentum, so I can imagine a trajectory that is basically outright perpendicular to the sun's surface. This will have you hitting the surface at around its full escape Delta V, which is 617 km/s. Your dynamic pressure goes with $\rho v^2$, so every particle that hits you hits with with about 10,000 as much oomph as particles causing atmospheric drag on the ISS. Because of this, the mass-thickness you could hope to plow through would be very little.
The density of gases around the sun's photosphere increases rapidly, but considering these numbers, not fast enough for you to get deep enough to do anything interesting, even with an insanely huge continent-killing bomb.
In these regions, radiative heat load would be a lot, but I disagree that it will be the dominating factor. Cooling can be done by boiling off some liquid that is stored on-board. This will work (for the purely radiative zone) because you're simply not spending much time within the area. Let's start with the assumption that the heat loads of Solar Probe Plus are survivable. The dive bomb would be going 211 km/s at the point it passes it perihelion. With this, I can develop a lower-bound estimate of 7 hours to reach the surface, more realistically like 3 hours. Yeah, it would be extremely difficult engineering, but reflective coating would buy you a lot, and active circulation of cooling fluid below that surface that is expended by boiling would help, and good insulation would also help.
But let's get to the point of this fireworks show. I'll say our goal is to create a tsunami wave on the surface of the sun that can be viewed with telescopic observations. In order to be "visible" this wave needs to be have a meaningful effect within the photosphere. I don't think this is possible. Ballpark a 1,000 km region within the chromosphere. Say it takes a 1 km/s particle to dislodge a single particle in the heat shield. The v^2 term gets us to a factor of like 360,000, and say the ablative shield can be 0.1 m thick. That will allow me to ballpark a tolerable mass-thickness, which combined with the 1,000 km assumption for the region's thickness, gives a density ballpark, of about 1e-10 km/m^3, or 1e-13 g/cm^3. This leaves us in the upper regions of the chromosphere before our craft is torn apart molecule-by-molecule.
I would like to get into the blast wave attenuation equation for this problem. I lack a specific viscosity for these regions, but it looks like it won't matter. It's hard for mechanical power to transfer effectively from the very low-density regions to the high-density regions, and we need this to create a well-observable event. Don't get me wrong, some wave propagation will still be happening through the photosphere, but it'll be relatively weak by that point.