In APEX, how do you drive an arbitrary channel of one or more controllers (e.g. rotation) using a different channel from another controller (e.g. translation)?
For example: A slider that rotates all finger joints.
Is it doable with the sops or I will have to use apex graph/script?

If You want to use a slider in APEX it would be a apex graph/script solution that modifies Your apex rig graph.
If You want to import sop animation You can use the "APEX Scene Add Animation" Sop in combination with a "Attribute Adjust Dictionary" SOP

I presume the question is to how to do this within an APEX character rig? Since you have animation inputs already for this, then I think it'd be easiest to modify the rig to just do what you want, for example see https://www.sidefx.com/docs/houdini/character/kinefx/customrigs.html [www.sidefx.com] for some ideas.