Doctors are completely used to giving people pills of some kind to delay their periods. I've done it about 4 times, for various camping/sailing things where it would just be annoying. You don't need to make up an elaborate reason, just tell them that you want to delay it for however many days.
I've never had bad pains after it, and because I remembered to take them regularly there was no issue at all.
Depending on how long you're going for, they might be reluctant (10 days is the most I've taken them), but the period doesn't start until about 2/3 days after stopping taking the tablets, so that's halpful.
I've been given different types each time, for some reason, but recently I've used "Norethisterone" and before that "Dydrogesterone". You could just ask directly for those, to prompt doctor. Maybe also see someone else who actually remembers their medical training?!
On a different note: couldn't you just have the period and deal with it? Unless you're in swimming costumes all day or camping or whatever, couldn't you just use tampons? Just a thought...
Hope it all gets sorted.
x