Bladdered has it spot on. This is why we have WOs who must (surely ???) be looking after sqn manning for the sqn boss. Your sqn cdr will have been round the block a bit and might have a 'bigger-picture' view than your shiny new flt cdr. I cannot recommend too strongly that you get your WO on side - and hence are a good lad (or lass) with a problem -rather than pulling in a lot of outside interference which will, if nothing else, deflect them onto to dealing with that rather than solving your problem.
I don't know your circumstances or your flt's op/commitments - it might be that your case might not hold up compared to others' problems or that your boss really does need (even a very unhappy) you to do some essential job or take your turn on det etc. However, if it is just 'I am short of people' your Boss need to get used to this for the next 30 or so years and this is the sort of training WOs are supposed to help JOs with, even if it does make their ears bleed.
Good luck anyway!