If ur shipping something "in", then shouldn't u be sourcing for boxes at the country of origin? But if u are looking for custom sized cardboard boxes in Singapore, I'd used Carton Express (www.cartonexpress.com.sg). Cost me about $30 to make a perfectly sized and fitted box for a guitar hardcase when I shipped a guitar to my cousin in the states.
Alternatively, u can also buy cardboard material and make it urself. There are plenty of supply stores in the Kaki Bukit area.