I'll be upfront out of the gate: sometimes, when I refer to my partner in front of our kids, I call him "daddy." I know a lot of you think that's creepy, but I don't. Despite your discomfort (which, I'll admit, I get) I have no plans to stop referring to him that way. Still, I see all of you. I see you and I care about you, you lithe and majestic squirrels, so I've come up with a handy list of names moms should call their partners instead of "daddy." You're welcome.
First, let me make a couple things clear so that, perhaps, you can understand why I don't think it's all that creepy. For starters, I'm not calling him "daddy" all the time. In fact, outside of the context of co-parenting, in front of our children, usually when I need something done for the children, I never refer to him as "daddy." In fact, I only call him that particular name in a situation like, "Daddy, can you hand our son that cup?" or, "Daddy, our daughter wants to play with you." It's performative — a way to cue our children in to show them how co-parents effectively communicate. It's also a nice audio cue for my husband to know that he's about to be asked to get into parenting mode (if he isn't already.)
Of course, if you're effectively communicating with your partner in front of your children they're going to pick up on those skills regardless of what you call each other, but this makes it a bit more intentional and conspicuous, just as "mommy has to go the bathroom" makes your own one-on-one communication more intentional and conspicuous. If I had to guess, I would hypothesize that we do this, probably unintentionally, because it mimics how children learning how to speak refer to themselves, i.e. in the third person.
But, OK, you find it weird. That's your prerogative. Here are some totally less weird alternatives to referring to your partner as "daddy."