Nothing will happen. It will potentially itch as the hair starts growing in and getting longer, but once it grows past a certain spot, the itching will cease. You just have to put up with it through that point and try not to scratch. Shaving/waxing/trimming that area is a personal preference and not a mandatory thing to do.
My doctor once told me that only some women shave, when I asked him how common it was. I think it's a porn thing -- women porn stars shave and get their vaginal lips surgically altered so their inner lips don't show, in order to be more marketable in porn because it fuels (some) guys' fantasies of being powerful over women the way they would be if the women were little girls. But, just like someone would say to a guy worrying that he needs to have a nine-inch penis to please women, porn is not the role model for real life. As my doctor noted (in a bored tone of voice, I might add), it's not the norm. Let it go, you'll stay perfectly clean if you take your usual showers or baths.
Nothing will happen. Just continue with your usual bathing and don't worry about it.
You know back in the 60s and 70s nobody shaved and nothing bad happened to them. I think you're really over thinking this.