For a beard transplant, what can I apply to my skin (safe/won't affect hair growth) to combat dry crusty skin on recipient area?

You should not have crusting after a week. If you're still having crusting you need to see your doctor.

If the "crustiness" is your skin, stop pouring water on it!  That will actually strip the oils off your skin and make it more dry!  If it is your grafts, ask your surgeon.  Usually after 2 weeks, the grafts are pretty set, so some gentle scrubbing will take away the scabs, but check with your surgeon first.  If it's just dry skin, any gentle moisturizer will work.  Baby oil will also help in the short term, and help get rid of the scabs.

Gentle washing is critical until all of the crusts fall off, We make a point not to allow crusting with good washing starting the day of the surgery and followed daily. When there are crusts present, you run risk of pulling out the grafts, at least until all of the crusts are clear. The you can treat your recipient area any way you are comfortable as you will not harm the graft buried below the skin