Some medical or kinesiology tapes are already attached to backing paper on the roll - I just save some of those to reuse.

I think parchment paper might also work well, since it's coated with silicone (which I think is what most "backing paper" uses). Or something like this: https://www.amazon.com/SLICK-PAPER-silicone-release-paper/dp/B01M2A56DJ You basically just need something "non-stick" that you can temporarily stick the tape to and peel it off easily.