What an Idiot: Yes, the Geneva Convention does permit that enlisted POWs can be compelled to work, but only work in specific industries that do not help the enemy's war effort, otherwise they are exempted. Such exemptions include public works projects that are military in nature, which the bridge definitely fits. Colonel Nicholson should really have realized that. (Of course this could very well be Artistic License.) In fairness, they do mention that the bridge will serve some non-military purposes such as transporting their wounded, but it really should qualify.
Considering the number of war crimes committed by the Imperial Japanese Army at this time, one might forgive the Colonel for being less willing to refuse the work since he probably had a good idea of the 'punishment' that might fall upon the troops under his command.