I'm with auntpiggylpn - just wet the seams and the paper should come off easily.
Like QuiltE, I take the paper off as I complete a block, usually by soaking it in my bathroom sink for just long enough to get it wet. I use thin plain paper though. Try it on one and if the ink doesn't run, you're good to go. If it does use the q-tip/paintbrush method. Under no circumstances would I try doing it in a washing machine.