Hmm this is a tricky one. I might try coating the paper after you print like with a couple of coats of spray acrylic.
It might make the surface tough enough so that masking will work for you without taking up the print. It might also make it waterproof enough so that you can just wipe the surface with a damp paper towel to get the smoke marks off, no masking required.
There’s also liquid latex:
Or even plain rubber cement. That might do the trick and then be pretty easy to rub off.
This issue speaks to me because I despise smoke marks. Definitely let me know if you try any of these because I think you’re the first to really ask this question.
@jbmanning5 was a Glowforge user for a long time and he did a lot of jigsaw puzzles. He has since moved on to a bigger laser, but maybe he will reappear to chime in on this if I mention him. It would be nice to hear how he’s doing anyway, he was a great contributor to this forum a long time.