Asa bald guy, I use a skull cap all the time (very hot where I live). I use the Castelli lightweight skull cap. Its thin but absorbs sweat. Important note- skull caps and helmets are like shoes and insoles. Changing the cap or insole may impact fit/sizing.
Another heavy sweater here, even in the UK I sweat a lot…
Bands do help, but reduced comfort for me. There’s also the convenience factor.
Recently switched to Giro Eclipse Pro (the aero one), and the sweat management is significantly better than any other helmet I’ve used, and I’ve tried A LOT.
I used it in 25 degrees at the weekend, and I do still sweat, but it’s channeled down the side of my face. Will probably pick up the more ventilated aeries for really hot days.
Id try a casquete and see if it works for you.