Savage chambered to 99 in 22/250 for a while. They are not all that common and can be a bit pricey but they are out there.

I bought a Bubba'd 99 take down in 22 High Power and rebarreled it to 219 Zipper which I use for much the same purpose as the OP suggests. I used a 1:8 twist so I can also shoot heavier bullets to duplicate the 22HP.