I was a total clutz at age 7, so bad that my mom wouldn't let me carry the eggs when we unloaded the groceries. At age 9 my mom signed me up for football. As we were not a football-watching family, the only thing I knew about it was that I could get hurt. But I did it anyway, and that was basically the turning point for me and athletics.
Your DS's response sounds like something I'd expect from my DD9, who is always telling herself she's no good at things, because of unrealistic expectations, which lead to task-avoidant perfectionism behavior. We have to PUSH her to get through that. We put her in situations where she has to try, and then, having success, we celebrate those successes, and remind her how her attitude was to start. It's a very long journey, and she's still capable of extraordinarily negative self-talk, but there are a number of domains where we've been able to tackle them in this manner, one by one, and seen our DD develop self-confidence and a growth mindset within those specific areas. As the breadth and scope of those successes increases, we're hoping she can stitch that patchwork together into an overall quilt of confidence (how's that for bad metaphors!).
So my advice would be, one, figure out how important this is to you and your DS. If it's the case that he really WANTS to participate and is holding himself back due to perfectionism and self-confidence issues, then I'd suggest it's time for a push. So, rather than saying, "Would you like to play sport X?", you could approach him with, "I want you to play a team sport this year. Which one will it be?"
And if it's not that he really wants it but is holding himself back... I'd let it go.
