No, I would not recommend it.
You could maybe go .17 HM2, but it's pretty much a dead or dying caliber now.
The problem is:
.22 WMR generates about 3 times the energy of the .22 LR.
The .17 HMR about 2 1/2 times more.
Even the HM2 is 50% more powerful.
That translates to more locking block force x 2.5 or 3 times, pushing on a larger case head.
(Bigger piston!)
Old gun, old steel, and not designed for those kinds of forces.
If I were you, I would re-line the present barrel in .22 LR.
In the long run, it will be cheaper, and safer.
And retain the appearance of the original barrel.
http://www.redmansrifling.com/relining_prices.htm
rc