get Emirates, Cathay, Singapore out of your heads. Especially the last 2 I mentioned. Even with 4000 hours, if you are not a citizen of those countries then you have very little chance.
Rubbish!! Cathay and Singapore Airlines are full of expats, at CX the expats by far out number the locals.
For Cathay you'll need around 2500 hours + to enter as a Second Officer. If you have some sort of Hong Kong residency you could get in earlier. I have friend who got in with around 200 hours AS A CADET WITH HK RESIDENCY.
From what i hear most of the expats at Singapore come in as Direct Entry Captains, not all on permanent contracts, not many expat F/Os. So you may need more than 150 hours for that one...
Emirates require a set in stone, solid as rock 4000 hours total including 2000 hours Jet and not an hour less....even if you're an aeronautics professor at Cambridge. I went to one of their road shows and they did say that they dont mind an expression of interest, but all their recruitment is done through their careers website, so letters may not be acknowledged.
Have you looked at Etihad? I thought they had some sort of international cadetship scheme going on. Best thing get some regional airline experience then hit the big boys in a couple of years. If BA hire again they have lower hours requirements than some of the overseas airlines + they pay better and will look after you as an employee long term better than some of the previously mentioned.........check out fragrant harbour forum for further evidence..
cheers.