Shouldn't be a problem - security at SIN is done at the gate, so it doesn't really matter whether you are transitting or originating in SIN, as far as that all goes.

Since your bags will be checked through, you won't need to worry about luggage collection, so it will be a simple matter of going trhough immigration (easily done), out through customs (nothing to devlare) and then you will be in the public area - should take all of about 10 minutes.

Dave