Moving, myself and my cigars

The only issue I can see it damage. I know what the airlines up here are like and they would be throwing my cooler around.

How many sticks are you talking about? A case like cigar caddy, while expensive, would provide better protection for them. Unless you have hundreds of cigars.

If you want to use you cooler maybe look at adding foam sheets to keep the cigars from moving around too much.

Also like tchariya said, watch the lid. Make sure you have the whole thing secure, with straps or tape or something.