Dont reckon that the fish mind too much. They are used to picking up dead fish, possibly with bones sticking out, bits of twig on it etc... dont think that a bit of wire trace is going to put them off at all.
I use QED wire for its resistance to kinking and thats pretty thick stuff. I don't seem to get poorer results than other people I fish with (except for Mr Edwards, but he always was a jammy bugger!) so my view is that wire thickness isn't a major factor in not getting runs.