Please advise what is the quickest way to heal a cut (minor)?

Simple rules. The real question is what not to do that slows down healing. Avoid using alcohol, peroxide, hibiclens, betadine, and bleach solutions. Inflammation ( red, hot, swollen, tender) is important to healing so anti-inflammatories (motrin, advil) are bad. Cover the area with a clean dressing changed every other day and protected from trauma. Antibiotics do not help healing unless it is truly infected.