I took the mini pill when on holiday when I was like 13. That's a lower dose pill which you take three times a day. I was given that pill because of my age, not because it was for a holiday however.
There's no reason (that I know of) why you can't take the regular pill to delay a period - if you are past the main stages of puberty. That's all that pills do - they delay periods, if you take the regular pill you can just take it for a week and not use the rest of the packet if that's what you want.
If you want to stop your period, you should start taking some kind of pill at least three days in advance of it starting for there to be no bleeding. Afterwards you stop taking the pill and after a delay of 3 days or so (that's how long it was for me but maybe it varies) you'll have a bleed that's more or less the same as a period. If you were on the pill long term then the bleeds in-between would likely be lighter than your usual period but it depends how you react to the hormones.
Anyway you should ask your GP and they'll give you the right medicine for what you want. You don't have to justify why you want the pill, they will just give it to you. And they won't giggle under their breath or make you feel embarrassed - though they may misunderstand you and try and talk you into getting the implant :P . Also there's no reason to be afraid of taking the regular pill - you're not "obliged" as it were to finish the packet - it's no different to the minipill that's just the one they give to youngsters.
(Also, I don't know if somebody answered already but riding pill packets is where you take the pill continuously so that you don't have periods at all, or they're more spaced out - and there's also no health problem with doing that)