Wooden flute care question

The part of the head joint around the embouchure hole gets discoloured by moisture from the breath and sweat from contact with the lower lip, and ends up losing its shine and looking, frankly, a bit sub-prime. What do people use to buff it up and keep it from absorbing moisture and then drying out, risking cracks? I use almond oil when I wipe through the inside of the flute, and give the outside a rub with it as well, but is there anything else specifically to look after the embouchure area?

Not that I am aware of.

I wipe the head with a wet cloth occasionally. I reason that some of the deposit in the grain may be water soluble rather than oil soluble. Sugars from beer for example.