This can not be done (yet). I did not come with a good way to quickly 'grow' the hair back, and not wait / skip days.
(Although this feature can be added if waiting is not a big concern)
Whatever you think works for the gameplay loop; you've already got it set up where there's normal body/facial hair growth over time as well as supplemental cream/medicine to speed it up, I'd think you could do something similar for the hair if you thought it made sense. Perhaps add room or character preferences for styled natural hair versus wigs.
Yeah I think growing the hair is not really as big of a problem as I imagined. I'll need to think about how to incorporate different hairstyles and colors into the natural hair path, but that may work in the end. A few more people also asked for the similar feature so I think it does deserve another thought. Thanks for reminding me about it!