I too have had a problem over the years when out with friends dining at a restaurant, and wine has been ordered. Everyone who knows me, knows that I very rarely even have a 1/3 of glass.
I simply order what I want, and if they re order something, if I want something I order then. Getting over my shyness, was a good thing, because otherwise I would be sat with water...... and I HATE, really hate drinking water!
If at someone's home, I either take my own, or ask for a coffee and if I know that I'll fancy tea, take some of my own, as I have a problem with tea these days sadly, digestive problems.
Truthfully, I don't like it when it feels like someone has gone out of their way to buy soft drinks for me, as I have to fancy what they have on offer, and often their idea of what I might like is way off the mark.
Re your ginger beer, sorry, cannot help mint.