In 2005 I checked in to fly ZRH-LAX and only when I got to the lounge did I think that I should have asked them to look up my AA booking/ticket to check the luggage through to my separately ticketed but essentially connecting flights. I brought this up to the lounge service rep and she called, had my two bags located, retagged and claim checks delivered to me in the lounge. I think you will have no problem having SWISS interline your bags to your separate Singapore booking, just bring a print out of your booking to make it easier for them to locate your booking.