I've done a bunch of multi color dip-dyes with contact paper. Just make sure you let the dye rest between colors. If the dye is not completely absorbed into the plastic, the adhesive can pull off the dye sitting on the surface and make the color look blotchy. I think the dip temperature plays a part in that as well (cooler dye = more time, but less chance of the existing dye bleeding back out to the contact paper)
Also, if you cut on the disc (I find it way easier), only apply enough pressure to cut the contact paper. I've never cut all the way through a disc, but if you push too hard, you can definitely see the cuts in the plastic...and that could affect the tournament legality of the disc.
All that said, I'd live with those risks any day over ruining the color by not re-masking. It seems like any time I take a shortcut, I only find new ways to disappoint myself.