It shouldn't be necessary to change the wheels at all. What I would suggest doing is run the inner ring (probably somewhere around 38-44) and get a smaller cog on the back. That way your chainline will already be much closer. When I converted my pug I used the original rear wheel, with no re-dishing, and used the inner ring. It lined up fine and I haven't had any problems with it yet.
On another note...
... Has anybody had to put a new rear outer brake cable through the frame? I'm not sure what the best way of doing it is and I don't want to spend hours trying stupid things.
It shouldn't be necessary to change the wheels at all. What I would suggest doing is run the inner ring (probably somewhere around 38-44) and get a smaller cog on the back. That way your chainline will already be much closer. When I converted my pug I used the original rear wheel, with no re-dishing, and used the inner ring. It lined up fine and I haven't had any problems with it yet.
On another note...
... Has anybody had to put a new rear outer brake cable through the frame? I'm not sure what the best way of doing it is and I don't want to spend hours trying stupid things.