Hi SunTzu
This depends - is your house a new build? Is that solid wall? Or is that a just plasterboard on a wooden frame?
If it is a solid wall - then yes you can use a wall chaser - I did - I hired one from jewsons - messy job (in terms of dust!)
Regarding the skirting - this is either glued on or is nailed on - either way there is usually a gap where the plasterboard finishes and the floor - cabling should fit in there no problem
As regards the floor boards are you chasing the wires to the other end of your room - if so the easiest thing maybe to route the cable wround the skirting to the other end of the room (provided there is no break in the route e.g. a door frame)
Best of luck - any other questions let me know