I haven't had any significant cuts in some time, but your heal time sounds about right, for the cuts to completely go away.

Depending how the severity I wouldn't shave for a couple days over that region, as not to set it off again, and I'd use an antibiotic at night until the cut closed, then a dab of Vitamin E to avoid scaring until I don't see the mark anymore.

Keep at it, and the frequency of these cuts goes down very quickly. Just be sure to avoid distractions...like singing along to your favorite song while shaving.