I'm thinking blue sticky-tack would work. It's supposed to be non-harmful.
For me the issue will be keeping a game set-up. Right now, I can set a bunch of dice on top of the maps, then put plexi on that, and the cats can sit on it to their hearts content without disturbing anything. That won't work with 3D. If I get bigger dice, they can get get their paws under it, and it will be less stable.
And I'm still going to get them and use them and figure out something.