Safety Knights

I do not think the "waiver" is an OSHA thing! If any task is voluntary and not directly work related to the employees job you are relatively safe from a recordable under 1904. Only scenario I can think would apply is as follows:
I am an HR Manager, and you are our EHS Manager. I just saw you leave with the Manufacturing Manager to play Disc Golf on our course at Lunch. I get a call from your wife and she tells me to have you come home it is an emergency. I go jump on one of the company golf carts to tell you!
As I approach the hole I think you are on I do not see you coming around a tree and hit you. I am thrown from the cart. We are both sent to the ER where we receive medical treatment above first aid. Under OSHA 1904 my injury maybe a recordable because I was doing something directly related to my job. Since you would be doing Disc Golf voluntarily, yours would not be an OSHA Recordable.
If instead you were taking a customer or supplier around the course, that might be a different story as that may be your job and a recordable.

1904.5(b)(2)(iii) would exclude this activity from being recordable, no waiver required.

A waiver might be helpful for other liability, but you're good from an OSHA perspective as long as it is voluntary.

Who knew Disc Golf would come up on Safety Knights? :) Cool to hear my employer isn't the only one getting involved in the DG Scene!

Agreed with all the previous comments, you aren't doing anything related to work so it's not an OSHA thing, rather a CYA that you don't sue the company if you were to get hurt on their property.

Make sure the company doesn't sponsor any prizes or competitions for people to play as an incentive to get out there and move.

Thank you for everyone's input. This had some really great information for me so I can go back to manager and tell him to let the team members use the course.