Do you really need 6 racquets while on vacation?
How 'bout just taking 2 or 3 instead?
In 2007 and 2008, I traveled to several out of state tournaments (within the US) by air. I also usually carry a 12 pack bag with 4 or more racquets when playing tournaments locally in the region (by car), but for these ones that I went to by airplane, I took just 3 in a smaller 6-pack bag. This lightened my carry-on load quite a bit, and since I didn't stuff it full, I was never questioned or asked to check it.
It's just my guess, but an international flight with a stuffed 12-pack bag would probably be a target for the airline to ask you to check it in regular baggage.
By the way, I'm not sure if it has changed, but my old college tennis coach used to fly down to Brazil every summer to help run a tennis camp. He'd always bring in a half dozen racquets, but almost always had to bribe the customs officials to let him through (since tennis racquets were very expensive contraband for the rich down there, and the officials assumed he was bringing them in to illegally resell). Food for thought if you haven't been there before...