I doubt it will have much of an effect since you have quite a bit of credit available.
You can investigate it by signing up at creditkarma.com. It will give you an estimated Transunion credit score (not identical to FICO, but probably a good ballpark). They have a Credit Simulator where you investigate the effect of different actions on your score (close an account, open an account, pay off balances, etc). It's pretty cool, although I can't vouch for the accuracy.
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