Hammond CV
That was the first model of Hammond to be equipped with the vibrato scanner. Models prior to that used a "chorus generator", which was a complete second generator, geared so that it ran at a slightly different speed. It produced phasing when it was mixed with the output from the main generator. That was a very expensive solution, which is why the vibrato scanner was developed.
The CV is a pretty rare model because it wasn't made very long. It wasn't produced until after WWII, and it was replaced by the C-2 in 1949. The CV is one of those weird models that relies on the tone cabinet for plate voltage, which is why the choices of Leslie that will work with it are limited. However, you can get a separate B+ supply that can be installed in the organ and takes the place of the b+ supply from the tone cabinet; once you do that, you have a lot more choices.
As for your Conn, I concur with the advice to play it for a while and see if the key contacts clean up. When I first got my Hammond A100, it had several dodgy keys. There's a procedure for shifting the busbars on a Hammond to expose new contact area, but I decided that before I messed with that, I'd play it for a while and see if it cleaned up. It gradually got better, and after about a month of playing, it worked perfectly.