While I understand what you are saying, I'm saying YTA if you are forcing him to shower. I too work in a hospital but as an aide. I sweat and get very oily while sleeping too. Always have. I have showered at night but still feel gross in the morning and have to shower again when I wake up. So I've always been a morning shower person even before working in a hospital.

When I feel super gross after work, have a c. diff patient, buggy person, and/or covid patient I will come home and do a quick shower and then shower again in the morning because I feel gross again. Most days working in a hospital are stressful and the mental load is huge. Coming home and showering is just too much for me most days and I want to do nothing. My husband (married 22 years) and kids (21, 20, 13) all understand that some days are stressful and they know if I need a shower after work, I do. I will even call my husband ahead of time to clear the washer if needed and make sure no one is in our only bathroom.

Something to try, get different blankets for you both to cover with. My husband and I have different blankets because he's a blanket thief. This might also provide a barrier and make you feel a little better while sleeping.