You may have one already. If you have a Lee sizer die with the tapered decapper (like in their 7.62x39mm and probably others), you can set the die to the point where it slightly flares the case mouth as needed.I'll get the die flair them.
Oftentimes, I use a 50 BMG dummy round to put a flare on the mouth (usually 6.5mm and larger) in a pinch.
You could do similarly to your .223 Rem. with any 30 caliber round with a FMJ bullet (anything that has the desired taper to produce a small flare).
Not perfectly precise, but you will run the near-completed round through a FC die (or similar) which will restore any slight imperfections.