In theory Wilkie, any running line will do just fine,You need to keep one thing in mind, that the thinner the diameter of running line you get although it might give you little greater distance will in all honesty be of a lessor breaking strain, and with Skagit especially, that could work against you.
Like as not, you will be using heavier /faster sinking tips and heavy flee's, so the chance of getting stuck into the "plug" now n again is a reality as is finding your self connected to a brute of a fish!
For anything Skagity I'd look to 30lb running line-if your using coated floating lines or 40lb Amnesia if your looking towards Mono!
That way you can comfortably use 20lb+ tippets if you need to and still be ok on all fronts.
I do use 20lb coated floating running lines on my switch rods, but as thats usually with smaller flee's and lighter tippet materials-15lb max. thats perfectly allright !.
Makes sense to me if your getting down n dirty with a heavy fast sinking tip and copper tube, your leader might take a greater amount of punishment than normal, so personally,I'd step up the diameter/breaking strain to suit!.
A Skagit line will shift any weight of running line you like. However, for the best turnover and loop travel you need a balance between slickness and resistance. For all the good reasons Rennie gives I would recommend 30 lbs, which will also satisfy the balance requirements.