I've never heard of discoloration because of trimming prints. I've only been doing my own darkroom processing for about three years, though, so I've not seen any long-term effects on my own prints. The problems I have encountered are trimming precisely (a little too big or small can cause problems in standard-sized frames without borders) and rough edges (caused by dull blades or worn trimmer surfaces). Neither is a big problem, IMHO.
One trick I use to help trim (relatively) precisely in dim darkroom light, or with color paper, is to lay down some painter's tape on my trimmer at the locations where I typically cut. That way I can position the paper by feel without squinting at the numbers, which of course are printed in low-contrast lettering on my trimmer.