JBMauser,
You asked the same question on the Single Shot Rifle Board a few days ago.
As I stated then, I will state again that the conversion is not a good idea. Gunnut69 is correct that the old Remington Model 6 was/is not stressed for the pressures of a modern .22 WRM or the new .17 HRM.
I don't want to sound like a broken record, but even a major manufacturer like Remington had it's share of difficulties in fielding for the 5mm Remington Rimfire Magnum less than a generation ago. All of the model 580/581 series bolt-action rifles were recalled for firing pin, burst rim and extraction problems. The 5mm RFM is now a dead end and cartridges are collectors items.
Gunnut69's advice to convert a Remington 580/581 is probably your best route if you are determined to have a customized .17 HRM rifle. It would probably be difficult to even FIND a qualified gunsmith that would be willing to tackle this project.