Probably a little late for you, but I looked into this situation before. As long as you are working in Singapore, you have to file SG income taxes even working for overseas entities. You have to pay CPF etc yourself.

One way you can save on taxes is you can consider setting up a local Pte Ltd entity wholly owned by yourself, that acts as the consultant for this overseas entity. You employ yourself as employee for this local Ptd Ltd company, where you are both owner and employee. This way, your highest marginal tax bracket would be capped at 17% corporate tax rate (taking Ptd Ltd profits as dividends instead of salary), instead of the personal income tax at 22%. This helps you when you get to higher income $160K per annum where the personal income marginal rate is >17%. Hope this helps.