First of all, yes, a payload can be launched in to space that would remain at the key altitude for a HEMP, and stay there for some period of time. This has been discussed in terms of North Korea, for instance, which has launched satellites into an orbit that a HEMP attack would be possible, although they likely don't have the payload capacity to launch a weapon in to that orbit today.
Okay, so how would one hide who did this? Hiding the launch is all but impossible, the United States monitors for launches continually across the world, due in large part to the ICBM threat. So one would have to launch a satellite that contained this as a secondary payload. Once the payload was in orbit, the HEMP payload would have to remain, something that large is essentially impossible to hide in LEO today. The track for the satellite would be well established for a long period of time in the future. That track would be tied to the country of origin.
Is it then possible to confuse who launched the attack? Well, maybe. The best way that I can think of would be to explode the weapon when it was physically close to another satellite. I don't know the accuracy of nuclear weapon detection systems, but if two or even 3 satellites were physically close, say, withing 10 km, it might be difficult to determine which of the 3 detonated the weapon. In particular, it might be an interesting scenario if there was both a US and a Russian satellite close together, along with this hidden device. It might be possible to track exactly what happened, but it would take some time. The primary satellite would be completely destroyed, the other ones would likely be in pieces, and non-functional, and even in different orbits, but given some analysis it would likely be possible to determine which satellite of the 3 was the culprit, although it likely would take hours to figure out.
Okay, a few more tidbits. The shape of the satellite might be known from the ground, due to advanced radar systems, which no doubt would be employed to their max for any "hostile" country's launch. Any such item would have to be disguised to prevent that, which might be met with varying success.