I looked at one of my teams that has a catcher who gets the bulk of the workload (around 86% of all innings), and four pitchers, over three consecutive seasons (Mantle, S31-S33).
The catcher is
Dean Schmidt. The pitchers are RHPs
Ronnie Gallagher and
Frank Petersen, and LHPs
Ed Jodie and
Bennie Walker.
Over those three seasons, the two lefties have the higher CS percentage. Walker at .480 (24/50), and Jodie at .459 (28/61). The two righties check in with almost identical numbers, with Gallagher at .298 (23/77) and Petersen at .299 (20/67). Though even those numbers are not really consistent as, for instance, Gallagher varied from .129 in S33 to .462 in S32 to .350 in S31. Likewise for Jodie, who varied from .560 -> .304 -> .538.
Probably need more data samples for other pitchers throwing to the same catchers, but if there's any correlation, it might be LHP having a better CS percentage than RHP. But we need more data to correlate.
As far as arm strength goes . . . the pitcher with the weakest arm in my sample, Walker (AS = 35) had the highest CS percentage. Jodie was next at (AS = 91), and the two righties were similar to each other (Gallagher AS = 54, Petersen AS = 59).