Kinokuniya book store at Ngee Ann City may well be your best bet. They had quite a few maps when I lived there. You would then need to go to an art store to get it framed... also in Ngee Ann City as I recall. Popular bookstore may have maps although I have never been there.
The reason shipping becomes hellishly expensive is that charges are based upon dimensional weight. The map itself ships cheap in a tube. As the volume increases, shipping charges rise dramatically. Therefore you should consider selecting and sending the world map in a tube... from here, for example (
http://www.mapsales.com/world-wall-maps ... ag=leftnav), then find a frame store in Singapore to do the actual mounting.