While your understanding is accurate and correct that a Bench Warrant from one state for a Misdemeanor or lesser offense will not be enforced in another state, the fact of the matter is you are being short-sighted by not taking care of it. Just think about what you've written here. You are worrying about whether you're going to be arrested because you have an outstanding Warrant for your arrest in NY - even though you're traveling to Georgia.
With the new TSA at every airport, if they check on you and your record for any reason, that Bench Warrant may come up and who knows what new impact the Patriot Act will have on your then. Its still too new to know what can happen these new days of terrorism and fear.
While I can't advise you as to exactly what charge you have against you without more information, I can tell you that it sounds like "Disorderly Conduct" which is a Violation and not a crime. I urge you to take care of paying the fine and putting it behind you. That Bench Warrant is liable to come up in your record at some other time and that will stop you from getting bailed out at a future time.
I urge you to take care of it as soon as possible. You won't regret it and you will eventually regret it if you don't.
As my colleagues have stated, you are wasting time and effort worrying about what might happen if you get stopped in another state. If New York wants to extradite you for your warrant -they will. The best solution is to hire a NY attorney to deal with your Long Island offense and clear your record.