That's the easy option. Back at the peak of my gym going days, a bit over 10 years ago... you could have your phone up there, but recording of any kind used to be banned. It was a gym that had youth groups and such going through (a police run club) so it was very zero tolerance. They'd allow you to sometimes record a PB, but permission had to be granted and usually the managers would record it for you which was actually great.

If you're recording content to put up on the internet, the least of your concerns are people watching you and it detracts heavily from real people living real lives who are just trying to do their exercise.

Hardcore gym goers back in the day would scoff at people being glued to their phones while training.