Fencing and crew have almost no injuries.
This is mostly true, but it made me chuckle. My daughter is about to have shoulder surgery due to a Crew injury. It does happen.
My oldest (boy) played basketball and football all the way through high school. Broken nose playing basketball. Broke his hand and his arm playing football. Also had a mild concussion with football. Scary hit. Helmet flew off. And he didn't get up right away.
My second (boy) was into soccer and Crew. Never had a sports related injury. Plenty of ER trips from playing outside.
My third (girl) played basketball and soccer for about a year and hated both. She ended up being very involved in Drama and Music. Despite not being involved in sports, she had stitches three times, broke her wrist, and suffered a mild concussion.
My fourth (girl) played soccer (hated it) and rows on the Crew team. She is the one about to have surgery on her shoulder from a Crew injury. It's rare, but it happens. She also had surgery on her wrist after falling from the monkey bars at school.
My fifth (boy) played soccer and did martial arts. No serious sports injuries. Lots of injuries just from being a kid. Broke his collar bone wrestling with his sister. And had stitches twice.
As a family, we run in local races and we sail! So far no major sailing injuries...just a couple of close calls.