the bore/grooves of an LR is a few thou smaller than the WMR. As such, you will need a reamer to suit.
It is a lot less than "few thou" smaller.
You are right that you may need a "reamer to suit", as it should be different
than a regular reamer used to chamber a designated 22 mag bore.
OP should understand that if his "single shot" is a bolt gun,
it might not have enough bolt travel to accommodate a magnum.
Diameter of the rim is also very different (magnum is larger).
Thickness of the rim is different (magnum is thicker).
So in addition to the re-chambering, a new pocket for the rim should be cut in the bolt or the barrel,
depending where the pocket is in that particular gun.
The extractor(s) might need some minor re-fitting, as well as the firing pin and spring.