Unfortunately, Lee doesn't make a push through die for .222". You'll have to find someone who makes custom diameter bullet sizing dies. I found one via google "Buckshot's" Custom Sizing Dies - Mountain Molds

I didn't measure the force needed to swage .005", but .001" will hardly be noticable.

While I won't recommend it to a reloader, I might try the .223" bullets in a .222" gun. One half of one thousandths, .0005" on each side of the bullet prolly won't make any difference in pressures.