You can try Hornady Unique case lube also on the inside of your case necks.
This is the best case lube in my books.
HOWEVER, when I use an expander mandrel to size the inside of the necks, I use RCBS liquid case lube. I put a little in a cap, not much,
I dip the brass neck in the cap, just wipe the outside, then I run it through the mandrel. I usually run the new brass through my FL die as well using the Hornady case lube. Afterwards, I put the brass in my ultrasonic cleaner to clean them up, then let them dry.
I have tried it dry, expander mandrel only, but something tells me dry on dry is "maybe" causing damage I can't see! Plus with the lube, it goes through the mandrel like butter!