Equipment – How Do I Clean a Refrigerator with No Removable Shelves?

I believe this has been asked already but I'll ask it again. How do I clean a refrigerator with no removable shelves? I am renting an appartment so this fridge isn't mine exactly. I have no idea what make or model it is either and I'm guessing it's pretty old (70s or 80s 90s at the latest). I tried to adjust the shelves when I first moved in bc they looked like they could come out and I can't fit tall bottles in there on any shelf. However, I was not able to remove the shelves because the fridge is shoved flat into a corner so the door won't open wide enough and the door including the shelves looks to be one piece. On the inside there is one glass or plastic (clear) shelf with removable drawers underneath but the shelf itself appears to have been screwed or otherwise permanently secured to the fridge. I can wipe it clean no problem but I'd rather not have to leave it open to dry for fear of it burning itself out. Also towles notoriously don't to much of anything in my appartment because I got cheapies and there is no airflow due to my appartment having all windows on the same wall and being located directly above the laundry room. My fridge isn't much better due partly if not all to it's age. So again, how can I clean it without ruining the thing?