Have you checked all your video settings in the game? If you reinstalled, then more than likely any custom settings you had are gone. "Stuttering" can be caused by alot of things, I dont see why they would be caused by skin downloads. I've heard other people complain about that but I've never heard a rationale to explain it. Even with a marginal system, the download shouldnt be that much of a hit on your performance. And didnt they make the skins available on the website for download all at once so you dont have to go through that? As for skins not being available in the CT, that happens from time to time. You just exit the arena and come back in, they work fine. One thing that can for sure cause stuttering like you describe is having higher max textures enabled than your comp can handle.
I hope this does you some good, or that the problem resolves itself. Maybe Skuzzy will have better suggestions. Good luck!