I've troubleshooted both those ideas, and actually made use of a Install/Uninstall tool from microsoft support (The actual name is lost to me). I was able to get WLE uninstalled with some effort, (after using the tool, repairing, then uninstalling.) Skype, however, remains an issue. Any time I try a fresh download and install, Skype merely stops working. I have no attempted a fresh install of WLE, but my assumption is that this will result in the same issue as before... I have not tried an old installation of Skype either, so I'll try that to see if it works.
My gut is telling me that this is an underlying issue, and though WLE and Skype aren't essential to this machines operation, I would hate to have the issue get worse.