No, you do not need homebrew to do OOT3DSHAX and Powersaves are a piece of hardware for the physical copies of any game to change saves, add cheats, create cheat codes, etc. (the other one is to install it through homebrew which does not require a powersave). To get a powersave just but one on amazon or eBay, they are fairly cheap. After you got a powersave just search up a video on how to install OOT3DSHAX using powersaves.Put aside $20/week and you could have it in a month. It's not that hard. Just trim off anything unnecessary from your expenses. Do you buy lunch instead of bringing it from home? Switch to sandwiches. Do you buy coffee while out? Give it up for a short time. Do you smoke or drink? Quit. Do you go to the movies? Don't. Before you know it, you'll be able to afford a Sky3DS. If you don't want to give these things up, you don't want to exploit your console that badly. If you have no unnecessary expenses to trim, then you have more serious issues to deal with and should probably sell your console to pay for living expenses.
Remember you can always sell the Sky3DS when you're done using it to downgrade.