It's all up to you.
Honestly I don't think the sitting on the sidelines aspect would be too bad. One season I got hurt and couldn't work in the park, but was doing other stuff around the mountain. Mostly scanning tickets with my good arm. Thought it would suck to see people having fun and being stuck there, but it was as close as I could get to shredding myself. It was cool to see everyone stoked and having a good time, talking to people about how the parks were riding, how different trails were, etc.
Your situation is a bit different because it could prevent you from skiing as much as you want, that said it really depends on how much you like those sports. Also what you want to do in life. Maybe you really like basketball and might want to coach in the future? This could be a good building block for that. Maybe it was fun when you could play but fuck that noise lets go skiing!
As far as your coach and friends just do you. Don't be a dick to people, but you can't skip out on the things you love just to please other people if it's not what you want to do. Once in a while helping out is different, but if you're going to have to make a commitment for the season, that you don't want to do, may keep you for skiing, simply because of your coach and the players, I think that's the wrong thing(imo).
Figure some things out and then talk to your coach. Just be straight up with him about things. If you don't want to do it, explain to him what's up, and that you want to ski etc. He probably won't be stoked, but at the same time, I don't think he'd want to do something you didn't like just because you though he wanted you to.
Also he might be offering it simply to keep you in basketball. If Basketball was a major passion of yours, he probably saw that, felt bad that you couldn't play, and wants to give you an in to keep you involved. Instead of you just sitting at home feeling bad, shooting all your basketballs and favorite pair of nikes with a shotgun or something and throwing your tv out the window when a game comes on.
If you have skiing and that's something you want to rock out, go for it.
"The mountains are calling and I must go."
- John Muir