I would agree with the others on not doing it, and using a more airline travel friendly option. Hunting packs suck as carry-on bags. And if you get the good 'ol TSA random check at security and swabs on the pack, it is not a stretch that they will pick up gunpowder residue. I carry ammo in my pack, I shoot off my pack, etc. so it is a possibility.
That will lead to really good times....
I am not sure what kind of hunt you are going on and the day hunt needs, but if you want something really light and compressible, that can do double duty as a standard "travel pack" when not hunting, looking to the lightweight backpacking industry might be an option like the Durston Wapta 30. Super light, compresses down like crazy, really durable textile and will handle day hunting gear (since you are not meat hauling with it) just fine.
Just keep in mind a pack/bag for airlines should not exceed 22 x 14 x 9 inches; that being said, I fly about 20 times a year, and always see some dumbass trying to bring a freakin' steamer trunk or body bag sized duffle on as a carry on. Nothing screams "I don't travel much, and want to piss off everyone in a 2 mile radius" than someone rolling in late with their neck pillow, crocs, a banjo and 48 oz water bottle lashed to their oversized POS backpack and then we all get to watch as they herniate a disc or shit themselves while dry-humping their luggage into the overhead bin. OK, rant over.
Check your hunting pack and all gear, and get a solid travel focused carryon. That is my two pesos of advice as a cynical traveler of many miles.