“When I’ve been in similar situations I’ve gone to the restaurant and just had Coke.”
Same here. And I have a baseball cap rather than a yarmulke.
Recently, at a professional conference, there was a reception in a non-kosher restaurant. The non-kosher restaurant arranged for me to have a meal delivered from a kosher caterer; it arrived at my table triple-wrapped with the kashrut seal intact. I still wore my baseball cap.