I think your question was legitimate. It is always good to know the Lay of the Land before going to some unfamiliar place. In the US, there are some pubic places that have gender-neutral facilities, but unfortunately it isn’t something that has been universally mandated. A few years back in Palm Springs, the regular sized Starbucks was replaced a new one that is probably about 5 times the size of the previous one. It was built with a really interesting restroom arrangement. The wash basins were external to the 2 completed enclosed and undefined toilets. Gender just never comes into play.
In the interest of full disclosure, I have been using women’s restrooms for about the past 7 years. It always seemed to me that I would be asking for trouble if I went into the men’s restroom dressed.
Anyway, in your situation, the only thing that comes to mind is the possibility of carrying a cane. There are foldable ones that don’t take up much space when you are not using it. That has the potential of looking very reasonable to anyone who might be watching. Unfortunately the downside might be having someone who was actually disabled waiting for you to exit, but it isn’t like you are going to camp out there…