My step-parent has always been referred to by their first name. I was like 9 when they got married so.. it just felt better than the alternatives.
My mother was always either mom or mother, I prefer mother now. She died in my early 20s, so I can’t discuss all my neglect-based trauma and get closure, and I deal with that by using the colder, less affectionate moniker.
My sperm donor (father) never really made an effort to be in my life so I don’t refer to him as anything most of the time. Doesn’t come up.
As for extended family, I don’t have much experience there either but my grandmother was nana, and my aunts and uncles are all title followed by first name, so uncle bob, aunt Cindy, that sort of thing. Cousins get dicy, because some of my cousins are my parent’s age. Anything iffy is just first names.
Did you know you can get pint glass koozies, just like for cans?
Eg
We also have those nice paper sleeves for coffee cups that would do the job as well. At least where you touch.
So it’s an already-solved problem for this application.