Some ideas I have:
NERF guns (of course with a lore-friendly name): Brightly colored toy guns that fire foam round. Do no damage when they hit someone but show a message in chat.
Fencing: Either as a Holodeck setting, or some fencing supplies stored somewhere, fencing foils would do minimal damage (not really any more then other generic stuff around the ship does. fencing armor would protect from it, safety first after all), but show a message in chat.
Football: Footballs that are kick-able like Schlorrrgos, and a football pitch holodeck setting.
More card games: I've seen a number of different card game types on different servers, some of those may be neat to port. One example is a game similar to Cards against Humanity.
Gym: Treadmills for the gym?