Probably a bit late with this post but will give advice anyway. First, do not use steel screws in oak - they will stain blue - use brass. Secondly, if you have a very sharp 1/2" chisel, it is possible to lift a small flap of timber, drill. countersink and screw, glue back the flap. Sand flush, or use a cabinet scraper, and it will be invisible.
Wow - now that would have been a great idea. Although I am pretty sure if I tried then chunks of the skirting will go missing).
The plugs are in. I just need to trim them to a sandable size now.
As for the screws. Now you may laugh but I have used 2.5" (60mm) (SIZE 10) - Twin threaded - countersunk head - hardened zinc plated.
These are countersunk about 4mm and will be plugged. Am I going to get blue stains ?