It's actually not necessarily a bad idea to have a general anaesthetic - and it's nothing to do with being a wuss. Sometimes, when the local anaesthetic is infiltrated, the surrounding tissues become engorged and it can make it a bit trickier to locate the vas. That involves a lot more er.... "manhandling" in order to get hold of it in order to make the incision, dissect it out and get a ligature or clip onto it.

That in turn can mean that theppatient has a lot more discomfort post-operatively too - due to all the additional manipulation that's gone on.
Of course that doesn't happen to everyone. Some men just need a very small volume of local anaesthetic, which means that the vas is easily found.
If you have a general anaesthetic, a little bit of local injected at the end of the procedure helps as lot, as the OP discovered.