You asked above "What would a trans swap do to the engine". Well, depends on how he did the swap. If he left the engine in and just pulled the trans and switched them - not much. But if he pulled the engine - a LOT could go wrong. Forgotten grounds, rough treatment of a 35 year old wiring harness, changed the engine computer to a manual model and didn't connect things right, etc, etc. You are wise to check the compression yourself as I have a suspicion the mechanic knows with all that going on he knows he overlooked something. And as stated, he knows the best strategy is to say "That naughty car broke itself while I was working on it. But I'd be happy to charge you to see what it did to itself".
What I'd also like to hear is how do you have a nonrunning car back from a shop? You gave him a running engine'd car for a tranny swap. He gave you back a nonrunning car with a different tranny and you said, what? - that's OK, I'll pay you and take the car home? So how did his test drive go to verify the tranny is fully functioning in all gears and at all speeds, etc.......cough......?