Before you start bending anything or buying anything, take a cheap plastic
vernier caliper (or a better one if you have it),and measure the rear dropout
width in your frame.. .. Then measure the over lock nut distance for your current
wheel and that for your replacement wheel.
In theory, the old for the wheel that goes in should match the dropout width
for the frame, but you can get away with a few cm difference either way.
Your bike might require a little resetting, or none at all.
If you do decide to cold set it bigger or have someone do it, read up on the
proper way to set up a string from the drops around the head tube so you get
the stays to go out equally on each side. Otherwise your alignment suffers.