perl -p -i.bak -e "s/\r//" filename
loops thru filename, removing the ^M characters (\r), and creates a backup with .bak appended to the filename-a commonly used one-liner to do the same thing. (.bak could be replaced with something else, or left off if no backup is desired)
Update: No need to feel embarassed-I would be willing to bet that most of us have written a script to do that same thing before. Appreciate the fact that you looked at a problem and came up with a good solution which dealt relatively effectively with contingencies, and chalk it up to practice in growing in your abilities to use perl effectively. Reinventing the wheel isn't always bad, if you gain a better understanding of that wheel and don't try to reinvent the same one too often.