I don't like WD-40. I stopped using it years ago.
Over time, it becomes a thick, gummy varnish. It will also creep in around primers and deaden them. I know these from personal experience.
For cleaning dies, I use brake cleaning aerosol or, for small tasks, Ronson lighter fluid and Q-tips.
Lighter fluid has a handy applicator to put just a drop on a patch or Q-tip, so spills or overflow are eliminated.
It's also good for degreasing chambers and bores before firing, which should be free of any oil or grease before loading. I keep a bottle of it on my reloading bench, and in my shooting bag.
Q-tips and pipe cleaners are useful for cleaning dies.
For heavy lubricant or lead ring deposits, use a bore brush slightly larger than the die's opening. Once clean, lubricate exterior and interior threads with a dry lubricant like graphite or molybdenum disulfide (allowing time for the carrier solvent to evaporate).
I avoid using any oils or greases in in my dies -- other than those intended for resizing -- so I don't run the hazard contaminating powder or primer.
I have some dies I've used since the early 1970s. With the above treatment, and proper storage, they'll last lifetimes.