Yes, there is a company who can ship fragile items from taobao to Singapore, DJcargo is the company which could handle fragile cargo shipping from China to Singapore by door to door delivery.

Sometimes you purchase goods from taobao and use its default third part logistics to carry the cargo directly from sellers' warehouse in China to consignee door in Singapore. and you may received notification that the third party logistics warehouse refuse to transport the fragile items. ... so how do you do?  don't be anxious, the next procedure you can follow to handle your item shipping out from China to your door in Singapore

First of all,  contact CS representative of DJcargo China office, to have a sales person guide you how to do it.

DJcargo is able to ship any fragile items from China to Singapore, but your goods must well packed, foam materials do internal packaging to protect it shocking, plywood do external packaging to protect its loading and unloading.

DJcargo also offer wooden crate and case packaging service, but the prerequisite is send to DJcargo warehouse is undamaged.