He sounds like a good enough swimmer to me. I wouldn't push it. He can always catch up if he gets more interested in it later since he's not brand new to the water.
Total side note-There is a boy in my 4 yo daughter's swimming lesson who cries through the whole lesson. Every day. His mom explained to all of us moms that he's been put in the water since infancy and he's always been terrified of it. She's not backing down and she's keeping him in lessons. However, he was crying in the dressing room after the lesson because he was cold, crying in the parking lot because he wanted ice cream, crying because they didn't stop at the swings on the way to the car, she was appeasing appeasing appeasing, telling him he did great at the swimming lesson while he cried about the swing and the ice cream...and oddly enough, the day his dad brought him to the lesson, he didn't cry at all. HELLO! TANTRUMS!
Anyway, this isn't your son at all, but you did mention you'd have a crying child on your hands if he has to go to lessons, and he screams if you mention it.
Does he ever cry to get his way in other circumstances? This would need looking into, as far as what's allowed or not by mom and dad.
But, if he's only like this about swimming, I wouldn't worry about it or force it. Find something else he likes to do so he gets something fun and new associated with his new home.