Not attempted that workflow, and probably lots of ways to solve it, here's some thoughts that might give a solution. Someone else might have an even better idea.
Here's a C4D scene and a PSD. The scene has a brick plane hidden in it just so I had something to render to use as a background that would match the perspective, but can be ignored for what I was doing.
There's a shadowcatching disk, which I used Rayswitch on so that it wouldn't reflect light onto the cube when rendered. It has an ID pass so I can selectively remove the cube in post. I can use the beauty pass and the cube ID mask to show just the cube without shadows. I can then either use the beauty pass, remove the cube using the ID pass as a mask, and then I get just the shadows which I can use Normal (or other variation) as a layer, and can adjust opacity to control shadow color. Or I can use the Shadows pass, do the same ID pass mask, and use Subtract mode with the layer, and then use Opacity to control the strength of the shadows (in this case, the disc doesn't really need to use the Shadowcatcher).
I didn't try and resolve the anti-aliasing question of the cube in this test (I also used white when rendering, but the saved scene has grey which should in theory be better for anti aliasing).
Both ways require just one render rather than two, and may give inspiration for how you might resolve it.