How to keep a palm thorn puncture site clean on scalp?

Hey,

My father (60sM) hit his head on a potted madagascar palm and got a couple thorns embedded in his scalp for the trouble. We cleaned the area with alcohol both before and after tweezing the thorns out and applied antibiotic ointment to the spots and will be keeping an eye on it for signs of infection.

Everything I've read about about palm thorn punctures says to keep them dry, but we're genetically incapable of sweating, so he can't exactly do that. Beyond just watching the spots, is there anything he should be doing to keep the risk of infection low? Is "antibacterial" shampoo a real thing or is that just a marketing ploy?

He's got the classic Old Man Syndrome where every injury can be taken care of at home, so it'll take a lot to actually get him to a doctor, but if he can do it himself he's happy to (for example he told me to shave his head if needed).

Thank you!