I have to find a new hairdresser every time we move. It's never much fun because I like to stick with the same person. But here's what I do. I get my last appointment one or two days before departure, and ask for it to be cut extra short. That way I have a little more than the usual four weeks so I don't feel quite as pressed right when we get to a new place.
In the new place, I look at other women's hair styles. When I see a good pixie, I ask to be introduced to her stylist. In some places, I don't see what I'm looking for on other women's heads so I just go to the nearest salon that looks reasonable and ask for someone who does short hair. I'm clear about what I want (super short on the neck and around ears, round on top but thin it out) and understand that the first cut may be close, but not perfect. I figure with feedback, they can get it right in the next appointment or two. After that, they just know.
It's very rare that I dislike a stylist, and when I do, it's been because of how they handled my hair (too rough) or how they managed the cut off bits (if they're all over my face, I won't be back).
While on your trip, you could ask a local stylist to just follow your existing cut and trim off a 1/2" or so. They should be able to do that without a problem.