How to clean consumable metallic parts cheaply while touring?
The most frugal is not to intensively clean these parts except at the end of the tour when you overhaul your bike. 

Simply brushing off the dirt with a cleaning brush, toothbrush, or rag and relubricating with a good dry lube will get you most of the benefits with little of the mess. And it’s a lighter kit. 

You don’t need a spotless bike.