since you are keen to work abroad, why don't you try applying overseas directly instead of limiting yourself to S'pore based jobs?

Europe and the US may be tough given the job market, but maybe Asia is an option. Look at Hong Kong - conglomerates like Swire (which is the majority owner of Cathay Pacific) or MTR have good management trainee programs and they take international graduates.

Swire also has a stake in Hong Kong Aircraft Engineering Company (HAECO), which could be up your alley.