Ironically, thanks to the potentially lethal weaponry used as equipment, archery and target shooting.

Swimming is also relatively safe. Distance running might result in repetitive stress injury, but it won't kill you.

Slow-pitch softball eliminates most of the risks from baseball. Hit by pitch and RSI from pitching are the dangers there.

Cycling removes some of the RSI risk from distance running, but replaces it with higher-speed impacts, usually into hard surfaces.

Edit: It depends on your definition of "team sport", really. If you define it such that you can't meaningfully separate out any individual performances, you're cutting out all relay-type competitions from the start. If you say archery is not a team sport, then neither is a swimming relay race. Where do you draw the line? What's the minimum number of participants that have to work together to qualify as a team?

One of the safest sports I've seen is oddly flag football. Especially for youth. There's typically no blocking allowed at the youth level, and obviously no tackling.

Of the youth sports I'm involved with flag football and baseball are the two safest (especially if you're not a pitcher). Then basketball sits in the middle as pretty safe. The main worry in basketball is running into someone going for the ball. I'd put soccer and tackle football as the most dangerous (tackle football being more dangerous). If they eliminate heading out of youth soccer, it would move it into the basketball level of safety.

I'm not sure there is any way to change tackle football to make it reasonably safe for kids.

I don't think basketball comes with a lot of TBI, and baseball is pretty safe if you don't get hit in the head by pitches. That's 2 out of big 3 in America.

Really? There's a bunch of non-contact or limited-contact sports.

Crew, tennis, baseball, swimming, golf, all of track and field, etc.

Volleyball is fun and challenging when played well. I'm not sure how easy it generally is to find good competition to learn from -- southern California where I grew up was a good place for it.

Baseball is definitely up there; catching and pitching can be a lot of strain on knees/shoulders but for the most part it's safe long term.

Basketball.