Using a Where and a SkipWhile doesn't result in "going over the collection twice." LINQ to Objects works on a pull model. When you enumerate the combined query, the SkipWhile will start asking its source for elements. Its source is the Where, so this will cause the Where to start asking its source in turn for elements. So the SkipWhile will see all elements that pass the Where clause, but it's getting them as it goes. The upshot is that LINQ does a foreach over the original collection, returning only elements that pass both the Where and SkipWhile filters -- and this involves only a single pass over the collection.
There may be a trivial loss of efficiency because there are two iterators involved, but it is unlikely to be significant. You should write the code to be clear (as you are doing at the moment), and if you suspect that the clear version is causing a performance issue, measure to make sure, and only then try combining the clauses.