I feel like if that was from a bullet, even from a very small round, that it would have caused more significant damage, as there’s a lot of very sensitive areas in that part of the skull. To go straight through like that would also very likely have caused significant bleeding, as there’s a lot of blood vessels around the face, so I imagine he’d have been a lot messier when you found him. If he was shot, he seems very lucky so far!
I think it might be more plausible that those are puncture wounds from being bitten in the face by a larger animal, like a dog as you suggested. Definitely worth taking him to the vet, tho. Hope he’s feeling alright!
I dunno how reliable it is, but I’ve had a lot of cats growing up, and we’d always try to get them used to water when they were still very young kittens, giving them baths in the kitchen sink. Most of my cats ended up tolerating getting a bath into adulthood (I don’t think any of them loved it, but they didn’t freak out about it), though we had one who was always a crybaby about it, from day one.
Sometimes you just get lucky and end up with a cat that absolutely loves water. I had one that I’d have to lock out of the bathroom whenever I’d shower, because she’d always want to get in the water and start rolling around and try to get under my feet.