No, there is no way to change the refresh rate on your ClickShare devices (except for CB Core/Pro¹) and also there are no plans to introduce this feature.
However, it is possible to change the output resolution for your ClickShare device. By default, the output resolution is set to Auto.

Note: To find out about the supported output resolutions for your ClickShare device and how to manually select the output resolution, please see the installation manual for your ClickShare device here.
¹ See KB 13362