You would at least require residence for COPA. I used to fly in Panama for a regional there as a training captain, and that was the only way I managed employment. I have a couple of friends at COPA on the NG, one is Columbian but married to a Panamanian, the rest are born and bred Isthmusites. If you had heaps of time and were a training captain on the NG you might be able to land a job as they have hired that way before, but only for contract. Continental does not have the equity they used to have in COPA, but still code share and of course COPA is Skyteam.
As a new pilot, if you really want to fly overseas your best bet is PNG or Africa starting on a C206; lots of jobs on that route. Forget about Cathay, Singapore or anyone else until you get at the very least some multi time, and better yet some turbine time. Unless of course you can hold Singaporian residence, then I'd apply for the cadet program.