Liner for Cage Ledges

Hey guys, so I just adopted a chinchilla from someone who was moving and they gave me her cage as well. Her cage as three built in ledges which is great but they're metal wire so I need to cover them with fleece so that they're not too hard on her feet. I know you can buy fleece liners from etsy but all the ones I've seen slip on over the cage or whatever. My ledges are built into the cage and only have one side exposed so it'd be impossible to slip anything over them. Does anyone have recommendations for what to do?
Right now all I can think of is to buy some fleece and place to over the ledges and just secure it with a safety pin to the outside of the cage. I am worried about my chin trying to get at the safety pin though.
I attached a picture of what the ledges look like so you can get an idea of what I'm talking about.