Didn’t a new prop come pre-lubed? Note Hartzel cautions to not over-lube.
I’d ask around at a prop overhaul shop. Maybe they can spare some. Have you tried calling NYCO?
"New or newly overhauled propellers should be lubricated after the first one to two hours of operation because centrifugal loads will pack and redistribute grease which can result in a propeller imbalance. Redistribution of grease may also result in voids in the blade bearing area where moisture can collect."