Without knowing anything about your relationship or the party it is harder to judge, but I don't immediately see anything too wrong with it.
Someone being unfaithful is unlikely to get a friend to take a photo of them together, it's more likely that they got on at the gathering and someone took a photo to remember the event.
Your bf invited you to the gathering, so they clearly wanted you to be there which is a sign that they don't have any ideas about cheating.
Ask yourself where you would prefer the hand to be. The hand on the hip is honestly the most normal hand position in my opinion. Around the neck feels too physically close and can be awkward. Around the waist could be awkwardly close to her boobs. The hip is a bone, so it's not sensitive or romantic feeling if you hold it, it's probably the least sexual way to hold someone.
If you know that your bf is usually shy, then he was probably just enjoying himself. He's bound to drink more if he's with friends and everyone is having a good time. In a social setting like that it's almost inevitable that you'll end up talking to new people, then someone might be taking photos that they send to people afterwards. He even deleted the photo, and he probably wouldn't do that if he had feelings about that person
Added bonus. It's a friend's cousin at a friend's party. There are many people who wouldn't want them to get together
You may not like the photo, but he deleted it. It's not weird for friends to take photos. Guys can have girl friends. Don't try and suppress that. Obviously there is a limit, but a photo is nothing
TLDR: He probably got drunk, met someone, a friend took a photo, he held the least romantic place, then got sent the photo, then deleted it.