CUtting out hair

hey there, i’ve asked this on reddit but the subreddit where i asked this at hardly ever gives me answers and my friend wants to get this done so i can get to working on other models,


(not sure if pictures really work from this link so ill just repost it https://preview.redd.it/tvnzcxzfs7y81.png?width=735&format=png&auto=webp&s=f3156b9bd9045b2d316a4605baacf2a7f2ed572a)

within this image, the outline from being selected isn’t exactly on the hair but generally around it, which is a problem because it transfers over to being black/white spots, or in my case the same color as the hair, i cant think of any solution that’d just cut the transparent spots for me since thats the only thing i can think of to resolve the issue.