It isn't shaving that makes hair coarse -- one shaves because the hair is becoming more coarse and obvious.
If hair is very fine and the growth not hormonally-driven, then other methods may be OK. If it's coarse, male-type hair growth, then shaving is sometimes the only effective answer.
A complete hormonal assessment is always an excellent idea and if the problem isn't of long standing it may be possible to reverse the situation by getting all hormones within the normal limits for females.