Always good to have a plan white turtle. I too wonder if you can skip the trip to the park.
But if not, just have a plan for how you will decline. No is a complete sentence, you don't need to offer an excuse.
I've found that when I use an excuse that is temporary (no judging if you do) that it comes back to bite me the next time. (You are still on that diet? Etc.) just something to think about....
In reality it is a bigger deal to you than to anyone else.
I'm on day 2. I'm so happy I am not hungover like yesterday! I am grateful to be sober.