I wouldn't force them if they say they don't want to do it. I also don't agree that if you don't start sports this young, you can't play and compete in HS and college. I'm on the 'older' side of things, and the only 'sports' available to girls when I was young were softball (I still don't care to play it) and baton. That was about it. With 6 kids, my mom didn't have time to drive all of us around. We rode our bikes or walked to piano lessons and scouts.
I didn't start on organized sports teams until I was in junior high. I competed in Jr. high, HS and college...without having the 'benefit' of starting much younger.
There are a lot of individual sports which might suit your sons better. Tailor the sport to their individual interests.
Also, you say it's for socialization, not for fitness, so it could easily be another activity that they might enjoy more. What about organizing playdates after school or on the weekend with a few of their friends? Something a bit less structured might be more fun for them at this age.
Maybe I'm missing something, but I don't see the point in forcing them to do something that is not 'required' like attending school. Seems like it would make everyone miserable, these things usually cost money, and it may really turn them off about participating in something when they really are ready.