Yes, some fitting may be required for even a 22/45 --> 22/45 or mkIII --> mkIII swap.
The mkII is also compatible if you dump the LCI.
The experts are on rimfirecentral and guntalk-online, remember that on a Ruger rimfire autoloader the upper half is the "gun" according to the clever folks at the ATF, so you'd need to get it in person or through an FFL.
A holster will wear these, too ... just so you know.