Hi Alex.
My husband has a urostomy. He too wondered about cleaning around his stoma, knowing that any soap with cream or lanolin cannot be used. Our ostomy group, which we belonged to at the time, sent out newsletters that included a doctor's comment on what he does. He has been a urostomate since 1980. I was trying to find his article but was unsuccessful. However, this is what my husband does after reading the article.
So, with his urostomy, he lost his bladder, so he pees into the pouch. When it's the day he is changing his appliance, he does so in the shower. The doctor talked about having many peristomal skin problems caused by seepage. The doctor found relief for skin problems using an antibacterial gel - Dial Antibacterial Hand Sanitizer. My husband luckily didn't have skin issues but wanted the area cleaner, so he tried the foamy soap and has been using it for 9 years without any problems. You can find the antibacterial hand sanitizer anywhere. We live in Ontario, Canada, so I buy it at Shoppers Drug Mart. It's worth a try.
Good luck.
Ostomate Spouse since 2013.