They do make 2 piece grommets for the studs and do use them so the wire doesn't get cut and you get shocked and start a fire. Some jurisdictions require metal conduit, like Chicago after the cow kicked over the lantern.
You can buy some plastic boxes with a metal flange at 90 degrees that can screw into metal studs if your local code allows it.
If you can't afford a few extra bucks for grommets and metal boxes, etc., then maybe this project is beyond your budget now. Do yourself, your family, future homeowners, and your neighbors(when they watch your house burn up) and follow all electrical and building codes without taking shortcuts.
Make sure you have a permit and it gets inspected. Your question is one of the reasons why I prefer wood over metal studs. Good luck after getting off my soap box.