No, you cannot remove them in any way. They are permanent. I do not think there is a spell effect that can remove either one and even if there was, you would need to mod one through trial and error. And spell modding is the most arcane, convoluted aspect of modding.
Curses and horror marks may be annoying, but they are in the end not dealbreakers. Not for me at least, but they may be for you if you indeed feel as strongly about it as your post indicates.
In any case, welcome to the forum and I hope you will buy the game and stay around.
