Repairing rusty cages

I have a few cages that were given to me that have metal cage floors that are rusty to the point that some of the metal has rusted away. I'm toying with the idea of replacing the floor, but not having experience in disassembling and reassembling cages, I'm wondering if there is an easier way to fix them. I see in one of the floors, it looks like the previous owner patched one area with a new piece of 1/2" x 1" and j-clips. I'm a little nervous about doing that, though, because I'm concerned about the rusty exposed edges of the remaining wire. In order to feel like the floor is sanitary again, I'd really just love to replace it, then perhaps make some nice fleece "rugs" to cover half of the flooring so that the chin occupying that space can use the floor bust still get rest for his/her feet. I have both 1/2" x 1" and 1/2" x 1/2" hardware cloth to do the job. If this were your cage, how would you fix a rusty floor?