Welcome to the club, I can't really play on other guitars. I would say out of 20 guitars I've played, I was confortable with only one of them.

About freezing infront of people, do like I do. Build yourself a good solo, or just some good tricks one after another. I always practice one "show-off" solo for those occasions. Most of the people that will ask you this are non-guitarist or beginners that are waiting for the chance to say they play better than you do.

I've never been asked by a experienced guitarist to show them my best lick. They just ask to jam along and judge you on more important things. Most of them also know that they can learn something new from another guitarist since nobody plays the same.