HI Dirk
I did exactly that several years ago , I was backpacking round south america got low on money and Caught the ferry there. Unless it has changed ??? you need to have applied for a Visa (cannot remember name of the work visa maybe P45 ??) and as long as the paper work is in you can work.
However this is hard to do as you need a Employer to put the visa in for you . what i would suggest is email every Dive centre in Curacao and Bonaire and ask for Job. Are you PADI OWSI ?? as most centres are Padi there !
I notice you have only done a few dives so maybe sell your self well saying you will work hard and lower salary, etc.
I have work all around the world first as a DM then Instructor and never applied for a Job always I contact the dive centre direct and ask for a Job - it's really a matter of if they need someone at the time (does not matter if a SSI, PADI, CMAS, Etc school say you are willing to do a Cross over at your expense and that will also help.
Thats my 2 cents worth hope it helps
Mark