You can get a tattoo of someone’s handwriting. You will need to find a tattoo artist who can work very precisely at small scale to bring your handwriting tattoo to life. Not all tattooists will be happy to create a handwriting tattoo so you may need to look around to find the right artist.
It isn’t rude to design your own tattoo. However, not all designs can be tattooed and not all tattooists want to use someone else design so you will need to be flexible. An artist will work with you and won’t be offended by your request.
Do you have to know how to draw to Tattoo? In short, yes. If you can’t draw you will be very limited in the types of tattoo you can do, and most people want custom work these days. However, drawing is a learned skill and you can improve your drawing with practice.