Did you have problems with other soaps or materials in the past? I make a rash in my shoulders and neck with some soaps, quite noticeable after showering where it looks like sunburns. On the hands I can spill nasty stuff (like solvents or bleach) and there is no reaction :/
But yeah the idea of washing with soap only one hand is great to troubleshoot the issue... I wonder how you would manage that though.... I mean ... how do you wash an hand without using the other hand?