.22 LR reloading kits do exist, and one was recently tested on CGN with a mostly favourable report made on its function.
For the effort vs result, I'm not heading that way for reloading any time soon. Besides, I have 4+ cases of .22 hanging around, so I'm not in a rush to get more. Buy it cheap, stack it deep.
As for an actual Sig 225, well, I'll let you know that The Shooting Edge brought some in several years ago with extended barrels installed. They sold for $1049, which is why I never bought one. I'm not sure how many they brought in, but it was a limited quantity. I'd start with calling them to see if they have one tucked away in the back of the shop still.
If you cannot get a 225, then the 226 is pretty darn close in terms of fit and form. They are still in production, and you can still get parts for them too.
The sub-caliber .22 slide is a darn good idea for it too.
NS