Negotiate for deletion no matter what you do! Paying it off will do NOTHING for your FICO. If your looking into any mortgages anytime soon they will more than likely require you to pay it regardless.
Does Cox still own the debt, with the debt collector only having assigned collection authority, or was the debt sold to the debt collector, who is now the owner?
Is Cox also reporting, or is the only reporting by the debt collector?
Finally, what is the date of first delinquency with Cox the led to the collection?