Although I myself am not bald, I found this thread interesting. But if I were bald, I would use a scented artisan soap. Maybe something from Stirling or Zingari Man or Black Ship Grooming.
I like Neutrogena Tgel when I have scalp pimples. And Dove Mencare menthol caffeine for daily use. A simple cleansing brush is also great for exfoliating.
This article has a chart for recommended bald head shampoos for various skin conditions:
Here are some best shampoos for bald head that help reduce dandruff, inflammation, itching and redness on bald, exposed scalp. Asa cosmetologist, I can tell you that there are several hair follicles on your head
my dandruff problem disappeared along with the hair. If I use a shampoo it's for the beard. I got a sample of Kiehl's Amino Acid Shampoo a few years ago. i'm still using it. I do use Noxzema for face and head