in short the 5,6 Vierling is a 22 Winchester but with a jacketed bullet and a nitro load when the old Win was a blackpowder/lead bullet cartridge only. When the hornet was created it got a thicker rim and the shoulder comes forward to prevent it be fired in an old rifle.
so far you have to reduce the rim thickness from 1,6mm to 1,4 mm on hornet brass.

http://www.municion.org/22hornet/Vierling.htm
http://www.municion.org/22hornet/22hornet.htm

in theorie bullet diameter is smaller for the Vierling - only .221 / 6,63 mm but slug the barrel

have never done it but its maybe possible to short the 22. Hornet sizing die 3-4 mm by trial and error until the shoulder is where the vierling should have to be. could be cheaper than bying a vierling die set.