I don't know for sure but I suspect you might struggle to get access into the lounge without a departing boarding pass.

There is an airside transit hotel that would be an option, or you could look for something reasonably priced on your first night in Singapore.

However, given I assume you'll be battling a big time difference the best thing might be just to swallow the cost and head straight into Singapore. It's a very safe 24hr city, so even if you don't want to sleep straight away, there will be things to do.