I remember getting weirdly cocky about the whole thing, resolving that I wouldn't be knocked out as easily as all those others plebeians. They asked me to count backward from 10. I got no further (or lower) than 8. Next I know, I'm in a room with a few other wisdom-toothless guys with spinning heads; a little bit later, good to go.
I really don't know much about anesthesiology, let alone about how they do it in your area. But what I wanted to say is that those people are professionals, I'm sure they come across people uncomfortable with IV on a daily basis, and they know what to do.
Danilo_G 