I can think of no safer place than Singapore for sleeping in the transit terminal. The transit terminal is very nice with showers, a pool, putting greens, orchid gardens and even a hotel that would be about $55 for the 7 hours you are there.

It may be even more fun though to venture out into the city and pull an all-nighter.

You may check in in the transit terminal I believe. There is not RCC but there is a shared club that you will be given access too.