I think your group at work needs to re-think this. Why do you need 32 bit and 64 bit OS available for each user? And, if that's necessary, why not go the dual-boot route? I don't see the advantage here of using external hard drives which can be used for different OS. Indeed, I see that scenario as being more hassle-prone than just using dual boot configurations.
And, if there's a need to frequently switch from 32 bit to 64 bit OS, or vice versa, I would be looking at setting up one of the OS as a VM (virtual machine). This would allow running two OS simultaneously on one computer.