Our vets find it much better to not anaesthetise for castration, but to do the job very quickly with a very sharp knife. We had three done this way this year, and there was no evidence any of them felt a thing. If you anaesthetise, they have to be handled twice, and held between the jab and the op while the local works, and that means a whole heap more stress.
However, if the vet hasn't done a lot of these, I'd prefer s/he used local too. It takes a lot of experience to do them as swiftly, correctly and painlessly as our vet does.