IF that's the cause of the leak, YES, you could do it yourself, BUT, you need a fairly good selection of small hand tools and some time like you said.
THE problem is recovering the freon that's probably still in the system [it's probably R-12 & expensive as you've discovered], then having it properly evacuted for at least 45 minutes and recharged, though this could be done by a shop.
IF IT'S the evaporator, I'd recommend replacing the
Expansion Valve AND the Receiver/Drier.....the expan. valve will be in your hand anyway and they do fail, and the Desecant [the drier component] of the Receiver becomes staturated with exposure to the atmosphere over time.....keep me 'posted'...jeffb