Regarding the relay, it's just pull out plug in and go so no special tools. They're both the B5, so it'll fit. Just find the relay.
However if it were the relay, you'd have other functional issues with other things as well. I.e. on my old MK3 GTI, it also controlled I think it was the climate control.
If the relay still doesn't fix the problem, it's most likely your wiper motor. I know for the MK3's, they tend to go out pretty easily. Did you notice the wipers slow down or just stutter for a second before they went out?
I just bought my B5.5 Passat, so I'm learning what has a tendency to going out often and what doesn't, so those are my only two ideas so far.