Most banks won't want to take the risk of being a second mortgagee behind HDB (especially when prices are rather high now - i.e. value of property may drop if economy tanks). If you try applying for an unsecured loan, two points:
1) Most probably won't be able to get that much. $200,000 is a lot of money to be lent unsecured...$20,000 maybe.
2) Even in the unlikely event where they decide to lend you, the interest rates will probably be astronomical due to the high risk which the bank is undertaking. So it won't be worth it in any case - and your monthly repayments to service both your mortgage and your unsecured loan will probably take off a significant chunk from your salary.
On a side note, I heard HDB is quite strict nowadays in terms of allowing people to over-extend themselves. So they might want to have some proof of how you are going to be able to afford the remaining sum when you are due to collect your keys. Not sure about this though...you might want to call HDB to double confirm. Do keep us updated!