I didn't have surgery with Satterwhite, but I was told to wear mine for 4 weeks minimum. Longer if I felt any additional need to wear it. I ended up having a lot of skin irritation from it and I never really swelled, so my surgeon let me take it off for good once my drains were out at 1 week post-op. I did put it back on for a few days with a t-shirt underneath because I felt achy.
I imagine if you're feeling fine and not having a lot of swelling, it would be fine to go without it for the time that you're at the park. I would consider taking it with you though, and ultimately I'd defer to whatever your surgeon says.