My 7 year old often needs moisturiser but she mostly puts in on herself these days unless she's particularly tired after her bath. Dad would do her back, legs etc if she needed him to for whatever reason but nowhere intimate. On the rare occasions she's needed anytime more 'private' (she had thrush a while ago after a course of antibiotics) I put that cream on for her, in private in her room but only after she asked me to as it was 'medical' and she was worried about exactly where to put it (she's autistic and has to know all the details of everything!). Even then after I'd done it twice and she knew where it needed to go, she did it herself with me supervising loosely to make sure it wasn't all over unaffected skin.
Even my (female) 4 year old now, on the rare occasions she's had a sore bottom, will ask me to put cream on it not Daddy. They do 'pants are private' (NSPCC) from a young age which is great! At 4 she also shuts the door to the toilet and says she 'wants some privacy!'.
I don't think it's odd if a Dad NEEDS to put a cream on a child, no more odd that if I need to do it. DH would do anything the children NEEDED him to do for them, even if he wasn't overly comfortable. But he wouldn't just do it for no good reason and they'd have always the option of doing it themselves if they can.
Equally, now they're past toddlerhood he no longer walks around naked in front of them or has baths with them which he did when they were tiny. He does bathe/shower the younger one as she's still happy for him to but he'll stop/just supervise for water safety in the bath if I'm not around once she'd rather he didn't. He takes them both swimming regularly whilst I'm at work. They go in the family changing booth with a shower in it. They're all happy with that, but the girls wash themselves, and he keeps his shorts on.
It's really important that children have the ability to speak up about who they show their bodies to and who touches them, and they know that they can say no, they're not comfortable. Although in some families everyone is naked happily in front of each other, and no one would think anything of what you've put in your post OP.
It's really the child's choice! If the child does it themselves when Mums around there's really no reason for the Dad to and if I was the Mum I'd ask him to get them to do it themselves at that age.