You might want to look into getting some perineal cold packs. They are most typically used by cis women following childbirth or other trauma to vulva, and are filled with a gel that I find less irritating than normal ice packs. They also have a washable sleeve that they fit into, so you don't need to worry about wrapping a wash cloth or towel around the ice for protection. Bonus - they can be warmed up if you need a little heat therapy, and they are flexible so they can be used on other parts of the body fairly easily. Got mine from Amazon.

BTW - from what I can see, it looks like you are healing well. Congratulations on being on the other side! 💜💜