Read carefully! It would NOT slip while it is playing! You do WANT it to slip when you are cueing it up. When using Turntables, you generally don't need a Controller as the Turntables act as the Controller. Long before Digital, laptops etc we have been using the wax paper and felt to cue up Vinyl. This is where the name "Slip Cue" was born. You can hold the vinyl in place and release on a particular note to match the other song on the other platter? I am surprised you don't know about this.
Here get yourself a drink and sit back and enjoy this video. You will notice that the platter never stops.
http://www.youtube.com/watch?v=tr3ftsCVXhc&playnext=1&list=PLA93E93493B10FAF4&feature=results_main
I believe I have said it many times that I don't mix .. but having played plenty on TTs, the wax paper still stymies me .. if it works for your slip cueing .. great.