Yes, you can wash by yourself first, then go to cut. Because in Canada, if you want to have a hair cut in barber shop, everything has price, such as hair wash, hair cut, dry...even in Chinatown. Enjoy your hair cut.
I don't anything about 烫发. One thing I knew is that everything is cheap in Chinatown, but you must find what you want. I got a hair cut in a western barber shop before, it cost me 60$, because I didn't know the trickery.