Would it be safe to use those stick on tiles to cover wire mesh on the levels of my rats new cage?

I was going to buy a Critter Nation cage, but then I remembered that I have an old plastic and wire rabbit cage that's much larger than the CN (48" x 36" x 36"). The only problem with it is that it is one level, so I'd need to add a couple levels to it so thy can enjoy themselves more. All I can think of to make the levels is hardware cloth but i don't want my girls' feet to be on wire all day (though the bottom of the cage is solid). I was thinking I could just use those stick on tiles from the hardware store and cut them to fit the new shelves. Would this be safe? I don't want to use wood because wood will absorb pee and it'll begin to smell after a while, and my girls tear fleece to shreds so I can't really use that. If tile isn't safe what is? Or, what could I make the shelving out of that is solid?