Thanks for the advice, guys. It looks like I'll be taking Skillie's option #2 for a few days at least until I have time to clean the headset, at which point I'll do it and hopefully gain a better understanding of how the various pieces interact as I take them apart.

On a related note, how feasible is it to clean and replace a headset without the aid of a repair stand? Would I be just asking to have bits and pieces falling everywhere?