The cheapest and easiest way to go would be Redfield's sight mount that bolted on, replacing the right side grip panel. They called it the No-Gunsmithing-Mount. I'm not sure if another manufacturer is producing something similar. With this mount you can mount just about any red-dot sight or scope you want, and keep the mount/scope/sight undisturbed when you switch slides.
If you have the frame drilled and tapped and a mount installed, you can switch the slide assemblies without removing the mount/scope.
If you use one scope for both cartridges, you'll of course have to adjust the scope each time you switch, as .45 and .22 have different trajectories.
As to red-dot sights, I'll leave that for someone else to discuss. However, you might want to consider Tasco's optima. It is very compact and can fit in the existing rear sight dovetail. Early optimas had problems, but Tasco replaced all the problem units without hassle. Of course, you wouldn't want to switch the optima from slide to slide every time you switched slides.
The accuracy of a scope mounted to the frame will be only as good as the slide to frame fit. If the scope is mounted to the slide (optima), slide to frame fit isn't as important.
SF
" I have a Kimber Classic with a 22 conversion. I also have bad eye sight. I am thinking of getting a red dot sight for my pistol. Which one do you recomend and will it work equally as well with the .45 and the conversion. Will my Kimber have to be drilled and tapped? And will I have to remove it when I put the conversion back on. Will i have to resight it everytime I change from 22 to 45."