It seems exceedingly unlikely that a Perl script running on a *nix system using standard Perl IO would add ^M characters to files. It is much more likely that the characters exist in the original files and that those files were generated or edited on a Windows system.

A simple test would be to create a fourth file that you write a few test lines to, then check that file for extra ^M characters. If they exist there is something weird with your build of Perl. If they don't exist then either the characters are in the source files, or you have managed to get your write file handle into a strange :crlf layer like state.