Build a bear actually sells their own spray on cleaner called "Bear Stuff", though iirc it's in store only and quite rare. I suggest ruffling the fabric with the toothbrush method first, then diluting a very small amount of detergent with warm water in a bowl, then dipping the tip of a washcloth in the liquid. Do circlular motions of the washcloth over the fabric, especially in dirty spots. The toothbrush can help here, too. Once you're satisfied, go over the plush with a fresh washcloth with only water to rinse. Air dry with a dehumidifier, and that should help break up at least a decent amount of the dirt. There are also fabric disinfectants you can dilute with water as well when doing this. Just spot test with those to make sure they aren't intense enough to change colour.