[Concern] How should I deal with the scar from palm surgery?

Recently, I developed a small hemangioma and had a simple surgery.

The surgery went fairly well and I am recovering, but since it's uncertain whether water touches that area, I wash my hands carefully, excluding that part.

As a result, the skin looks dirty due to ointments and bandages, and the surgically treated area feels like dry skin peeling off in a scaly manner.

I didn't intentionally peel it off, just disinfected and left it alone, but it definitely looks messy and awkward.

What should I do in this kind of situation?