You are well within your rights to use the handicapped stall. It’s an accommodation not a reservation.
I'm a man, but I have always understood the dynamic to be completely different in (U.S.) women's restrooms. There, women chitchat with complete strangers. In that case, the current user would cheerfully respond, "Yes, I need a few more minutes" and that would be that. No embarrassment whatsoever.
Reminds me of the episode of IT Crowd where Roy pretends to be disabled.
This was an episode of curb your enthusiasm.
https://m.youtube.com/watch?v=mPzjbXgaVOk