Personally, I use baby wipes to clean my stamps. If I use Stazon I use the cleaning solution, other than that baby wipes work fine for me.
I use the stamp cleaning solution that Michaels sells and some paper towels to clean my stamps and have had no problems doing so.
I have used wet wipes for years, and have had no problems with them. I cut a small section off at a time to make them last longer, and they clean the stamps really well, and last a long time. I am with everyone else, I want to take good care of my stamps, and they seem to do a good job!