I see no reason you cannot use some other material. I get cotton flannel at Walmart. I do not care for the feel of wool. Very cheap for a yard of flannel. I do store the soaked pack in a Tupperware type bowl in the fridge and it keeps a long time. I do get many uses with the same pack. No need to change it after each use.
Below is a thread from long ago about this subject. This thread was before I found the flannel at Walmart. Hopefully you can find something there.