I believe that the bullets are different diameters which would screw up accuracy for the smaller 22LR bullets. However I think Ruger makes a single action revolver that has interchangeable cylinders to shoot both. You cannot mix and match in the same cylinder, but you can shoot both in the same gun with the correct cylinder.
Not the same round. WMR is much longer so it will not chamber in the LR chamber. JJ is correct about Ruger. They make a Single Six with interchangable chambers. They also made a Bearcat with two chambers, but it's now only available in LR. Colt made a very nice scaled down version of it Single Action Army called the Peacemaker in a .22 with two cylinders. I believe the bullet diameter is the same for both.