Given you have separate tickets, I imagine that your bags (if you have any) will not be through checked, so you will need to enter Sri Lanka, claim them, and then check in again at Departures. This is a pretty straight forward process and there is not much walking involved.

The transfer desk is run by SriLankan Airlines and could possibly issue boarding passes for you, if you do not have any checked baggage.

However, I really don't know if SQ is one of the airlines that SriLankan will do this for, perhaps someone else can comment? If unsure, go to the transfer desk and ask. If they won't issue a boarding pass, then you would have to enter Sri Lanka and re-check in.