You will be fine, good luck on your trip. BTW, to avoid a pointless argument with uneducated ground crew...if they ask, say it is bike PARTS. Otherwise they will try to make you pay the bike fee (which, as we know, will not work since the bike is inside conventional luggage that you do have the right to carry)...but one wise man once told me, to avoid conflict, just say bike parts and you will be done sooner.