A Muslim should adopt pure and halal source of income. It is recorded in hadith that the part of the body which is nourished with haram wealth the hell fire is suitable for it. You may open hair salon shop but you should avoid cutting hair in unlawful style. It is unlawful and sin to cut or shave beard and its income is also unlawful. You may cut hair but it is makrooh to cut the hair in resemblance to the fashionable and transgressor people against sunnah in different styles.
Allah knows Best!
Darul Uloom Deoband