You can run this on the live draft applet, but your absolute best bet is to use the slow draft/e-mail draft. For this, all you will do is go to the Players tab, hit Commish Draft, and draft for each player. If for any reason you make the wrong pick, have that owner log in and cut the player (you can cut the last player in a slow draft). Using the live draft applet would not really work because the computer would only think you are signed on and you'd either have to pause the draft applet very quickly and make the pick or keep undoing picks.
Definitely suggest using that method of drafting. It's slower, more fun, and you can see the whole draft board this way.
I can send you screenshots as well: fleaflicker.com