Chris
Before you start you need to determine exactly which particular 220 Wotkyns-Wilson Arrow you want to end up with. It is a wildcat, and as such, everyone had their own idea of what it should look like. The original, designed by Wotkyns and Wilson, used the same gauging point on the shoulder as did the Swift, but increased the shoulder angle to 30 degrees thereby lengthening both the body and neck lengths. Case taper and case length remained the same. Case capacity also remains unchanged. A 220 Swift case has to be sized before it can be chambered and fire-formed. (OTOH, an Arrow case can be chambered and fired in a Swift chamber and an original Swift case will emerge.)
There are also any number of "220 Arrows" out there that do not conform to the original. Most are mildly improved forms of the Swift with slightly sharper shoulders and/or lengthened bodies. Most can be fire-formed simply by shooting a standard Swift in the new chamber. The Ackley and WBY Rocket are the two most popular. I have a modest wildcat cartridge collection and I think I have at least 4 or 5 "Improved" Swifts and the same number of "Arrows". All different.
Exactly what do you hope to gain by re-chambering to the Wotkyns-Wilson Arrow, other than the name? Wilson hisself never claimed any ballistic advantage over the standard Swift. He was a cantankerous old SOB who, I think, designed his case so that the standard Swift could not be fired in it, just because he could. It gave him pleasure to pi$$ off other shooters.
So, bottom line, you'd be well advised to take Charles' advice and cut a test chamber in a barrel stub, make a chamber cast, and see exactly what you are up against.
JMHO
Ray