You could use leather balm. Rub it in carefully with a soft tissue. Or try Ballistol universal oil. I tried it out on one of my caps - it didn't do any harm to the leather (I was sceptical as I knew Ballistol only as lubricant for arms) if you scroll down here a little: Ballistol Universal Oil 100 ml dropper bottle to "Materials" you'll find the description for leather care.
I am old skool, and do not try to restore my caps.
A lot of conditioners have petroleum products which are not good for 80+ year old leather.
They also say to stay away from anything containing Lanolin or neatsfoot oil.
“Show me the regulation, and I’ll show you the exception.”
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