I've used Goo Gone to remove stickers like those on Gtb aprons, with no ink loss. And by just letting it soak, often I can lift up the stick intact, and then glue it back down on an index card or something else to save it. Then I just keep it with the game paperwork.
I even use some Magic Eraser to clean up the apron with water.
The problem with the ink is any type of solvent, degreaser, or such. Goo Gone and Goop hand cleaner both seem to work OK. But alcohol, Simple Green, Krud Kutter, any of that type of stuff will wipe off the ink in an instant.
The only issue with removing the stickers is that if the rest of the apron has yellowed at all, a 'shadow' can remain where the sticker was.
It's fine to leave them on though. Some stickers are more interesting than others.