I would not run a high C and a low C battery in series.

The reason being that the higher C battery can flow more current than the low C one. The circuit they are in does not care about the batteries ratings, it only wants to draw the current it needs. If the need is higher than one battery can safely provide but the other can flow the higher current then the higher C battery will still flow the higher current - through the lower C battery. And that will damage the lower C battery.

Runnig them in parallel would be fine, series, I would not.