If you have a Costco near you, I use the white terry towels from there. They come in a package. I typically throw them in the washing machine, then dry them and have had no problems with shedding. They work great. I have also have used regular cotton t-shirt material with success. You can also use cheesecloth. All depends on the look/texture you are going for.
I have no idea if these will work for faux or not, but we use mifties for all delicate wallpapers, pulps, murals etc. They are micro fiber towels that were originally used for car detailing. I love these things, and haven't grabbed for a sponge in months. They hold like 10X their weight in liquid. Can get them at Wally World for around $10-12 for 2 dozen. The ones below look exactly like the ones we use.
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