The "special dividend" would be the US income amount - that is the amount upon which the withholding was based. The 30% withheld is typically the tax due on dividends unless you are a tax resident of a country with which the US has a treaty to tax the income at a lower amount. The US doesn't have such an agreement with Singapore.
Individuals filing form 1040NR are allowed to take a credit for taxes paid to another country, however. The only real way to determine if there is a refund is to prepare the return as if you are going to file.
Note that you need to prepare the return fully and submit it, along with the Form W7 and supporting documents to apply for the ITIN. You don't get the ITIN first, but at the same time as filing your first tax return.
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