What Army regulation addresses high-risk activities while TDY?

It's the old, "they can add to but not take away" deal. There may not be a specific regulation that forbids it, but Commanders are given pretty wide latitude when it comes to enacting policy regarding safety. There's no regulation that states you must wear a reflective belt over your body armor after dark on a FOB in a combat zone but that doesn't stop some BDE/DIV CSM from making it a policy. lol

It is all based on risk mitigation, your base command and that if the command you are supporting. The bottom line is that is you are TDY and cannot perform your intended task because you were injured in a hi risk activity you Are subject to be found negligent during a line of duty investigation. Dove later.

No AR, other than safety. However, there is no difference between Sky Diving at duty station or TDY location. Unless is forbidden to SD at Duty Station too. Of course. If you will "add" just let it make sense. Dont add crap just to add.