I can't imagine the situation where a child would be devastated by not being able to play a musical instrument for 6 weeks, but also have the time to take part in a sport at such a level that the nature in which that sport is played would make it likely that they would have a serious injury.
In situations where playing a particular sport might be a problem (your child goes to White Lodge, your child is a chorister, your child is an Olympic gymnast, your child is going to appear on Young Musician of the Year), I imagine there will be a coach/music teacher available to force the choice with little parental intervention.
I can't think that sport/life was safer back in the 80's when I was at school, but I can remember very few children breaking arms/wrists/fingers etc anyway, and I can't remember anybody doing this on a sports field. (I remember more people have glandular fever than breaking arms).
pianomama, to me it sounds as though no doting was necessary on your part. Your son is perfectly capable of deciding what he wants to do by himself.
To be honest, I think that "should I ban my musical child from contact sports?" can be crossed off the long, long list of "things a parent has to worry about".