I want to route ethernet cable to a few rooms in a fairly small house.

Taking up floors is not an option because of wood flooring and I don't
want visible cable although routing cable around skirting boards may be
the easiest eventual solution.

There are aerial points in the house and the cable is routed within the
plasterboard wall of the timber frame house.

If the coax cabling is successfully dropping from the attick to the
ground floor through the wall (and from the attic to other rooms) I am
guessing that there is a clear channel within the plasterboard walls
which in theory I could squeeze the ethernet cable into.

Has anyone done this?

Presumably I would need an ethernet router in the attic to split the
single feed cable from the main modem/router into individual feeds.