We faced the same issue. I found a photographer that was experienced in photographing special needs children including children with ASD.
She did a wonderful job capturing my boys. She said that she had found some children with sensory issues don't like the click that the lens makes on the camera that most people aren't even aware of so she always brings her long distance lens so she doesn't have to be as close just in case. Next we found a pretty park & let the boys play. She worked with what they gave her just playing. It was awesome! We got some great pictures but best of all my boys weren't stressed with a studio & actually ended up warming up to her & enjoyed their play date with the lady with the camera. Hope that helps.

My son hates it also, but if we ask him first and tell him "Just one" it helps him to cooperate

That's great! My daughter freaks out just over the word picture. She wants no part of anything pointed at her. U can sneak and take one with out her knowing it with ur phone sometimes. U never really get a good picture. Most of the time she's like put up your phone Because she thinks u might be trying to take a picture. Thanks so much I will keep that in mind for future references.