Beauty must be a bilingual thing. At least that's the impression one gets from looking at signs outside hairdressers, beauty parlors and similar types of businesses in Japan. Commonly titled "Beauty Menus," the main function of these signs is to provide a list of the services a shop offers and the prices that will be charged for each of them.
One characteristic of the beauty menu is that it is commonly full of English loanwords. The most basic service, obviously, is a cut, which is カット in Japanese. In addition, you may have your hair shampooed (シャンプー) and blow-dried (ブロー), get a perm (パーマ) or some other treatment (トリートメント), or have some makeup applied (メーク).
This heavy reliance on loanwords on a beauty menu leaves room for but a very few distinctly Japanese words. One of them is shukumō kyōsei (縮毛矯正, hair straightening), which is something you can do when you are unhappy with the curls of your "natural perm" (天然パーマ). A related loanword is available here too, ストレートパーマ (straight perm), but this latter type of application is less durable in effect.