I don't know if that is what you were looking for, but here are a few action scenes I had in my stories that did not involve (too much) violence:
- Chasing sequence on board a space stations (with lots of bystanders)
- The characters taking some time off relaxing and skiing in the holodeck (there was no malfunction, only some nice falls and one character asking the holodeck to add a yeti to make things more interesting)
- Characters on a diplomatic mission engaging in some exotic sport contest on a planet (for their own fun but also for some diplomatic purpose)
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett