This issue's caused me a disproportionate level of anxiety, but it's an issue nonetheless and I wonder if anyone has any tips on doing quick gender swaps while out and about; I've pretty much given up.

While I'm
more than content to be out and about as a girl, I only do so when I'm not being called upon - usually by the JobCentre, with whom I have not yet changed my details. I only just received my deed poll, and so have yet to notify any government departments of the change. I don't feel great about presenting a false, male form in their crowded office, but I feel worse about having to explain why "Mr. Name" is presenting as a woman. I'm taking the easier option for now until their records are updated and they're calling upon "Ms. Name".
This causes me a problem next week, as I'm trying to fit social stuff alongside a meeting in which I really don't want to be a woman answering to a masculine name. I can dress fairly androgynously (and am still read as male), but the last few touches which I feel make me whole are not the sort of thing I wish to add in some mens' room cubicle - and sadly, the disabled toilets in my town's shopping mall are locked with a 'RADAR key'. You have to apply for those. >.<
I've resigned myself to heading back home, changing there and heading back out again, but I wonder, has anyone found ways to accomplish this?