It would work a lot better if you weren't actually bluffing, because you would take it a lot farther.
Don't worry about it hurting the age of you accounts in the short term. It won't affect the average age for another 7-10 years, not sure the right number for it to drop off. The only reason you should keep it open is if it were one of your few oldest accounts. If so, you could try bluffing anyway.