It's not surprising to find skin improving after the use of an anti-fungal drug -- many of them have a slightly estrogenic effect which is beneficial to the skin.
And more estrogen being delvered effectively to the skin will certainly reduce testosterone-fuelled hair growth.
For myself, I'd sooner leave my natural hormone balance as it is and shave -- I think most women are way too uptight about shaving facial hair. If the growth is very light, it may not be the ideal solution, but if the growth approaches male levels, it makes excellent sense.