This could be my memory and I could have missed something, but I know Balter requested a nuclear warhead from Adama to use for the Cylon detector (which worked, but which he claimed didn't work). It's never clear that he used the entire warhead and I always thought it was this warhead that he gave to Gina Invire.
Don't they keep track fo all the warheads on the Galactica and the Pegasus? Wouldn't they be able to show that the only missing nuclear warhead was the one Baltar had and trace it back to him and prove he was connected to the explosion?
Or did the warhead come from somewhere else? And, if so, where did it come from?