Sizing 223rem boolits to .224
Vlad,
You may be OK, with sizing your boolits to .224 for a bolt gun. SAAMI specs groove diameter for 223rem at .224
The general rule of thumb is to size GC'd rifle boolits (for non-autoloaders) to groove diameter or .001 over, assuming you are seating to a COAL where the boolit engages the lands during chambering.
If you are loading your ammo, so there is a jump to the lands (typically done for Autoloaders, but some folks do that with hunting ammo in Bolt guns as well, for reliability), then the rule of thumb is .001 to .002 (or even .003) over groove diameter.
With that said, you may want to slug your barrel, to verify exactly what your Groove diameter is.
If you plan to PC after sizing, that will change everything, depending on PC thickness.