Howdy and welcome to the forum,
The 17HMR is pretty much a 22 magnum case necked down to 17 caliber. It offers a higher velocity and a flatter trajectory than the 22 magnum by sacrificing bullet weight and energy. It is a inherently accurate cartridge in the many rifles it is offered in. I don't hunt with mine, but it is often used for hunting small varmints such as prairie dogs. It is more expensive than .22LR. I pay about $10 for a box of 50. If you want to shoot this round I would recommend just buying a new rifle. There are some people here
www.rimfirecentral.com who have made extensive modifications to a 10/22 so it could shoot the longer magnum rounds. You can also buy a conversion that will allow your 10/22 to shoot the 17HM2 round. It shorter than the 17HMR, being a .22 stinger length case necked to 17 caliber. Hope this helps