I think requirements are reusable, simple, small-size and things-to-easily-to-carry. There are exotic answers with chain clearers and other things that do not qualify to me simple. Perhaps, the Sheldown-Brown's shake is closest, here, to clean chains and then lube -- you can get bottles everywhere and alkali/white-spirit-whatever available to the bottle. But there may be more solutions. How do you maintain chains during touring? (open question: no season specified, etc)
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Met today traveling heroes, they offered excellent way to clean dirty chains, cheaply and world-wide-reusable -- a really good touring tip coming! Things you need are mostly-grocery-store stuff, good because you don't need to carry extra stuff and you cannot be sure of bike shops in all of your destinations.
I can guarantee the tip works: the chains initially were in very thick black layer. I tried also Sheldon Brown's shake with coco bottle but it failed to remove the dirt, this gentler way with brush worked better. I tried the tip and my chains become like new, love it. So No to pling-pling degreasers and cleaning containers during touring, no extra stuff.
My preferences is to use a wax lube every day and just apply, ride, wipe and ignore. But that fits with my style of touring - I free camp and usually get up, pack, ride then eat. So lubing my chain every day is part of the pack out ritual. But it also depends where I am and what I'm doing. In much of the Australian tropics a sticky lube will not work because the dust is iron ore, so sticking that dust to your chain kills it (the dust also dyes everything you own a dull orange brown). In wetter country a wet, sticky lube might work better but at the cost of greasy chain marks on whatever it touches, so I usually stick with the wax lube. Any solvent based lube has the advantage that it can be used to clean your chain, just by over-applying it and wiping immediately.
The difference between this and commuting is that I don't maintain my commuter bikes anywhere near as often. Sure, technically "every 100km-ish" is daily on the touring bike and weekly on the commuter, but my commuter gets maintained when I remember, or when I notice something wrong. I ride past several bike shops every day commuting, but generally have no idea whether there's a bike shop at all when I'm touring.
I'm currently experimenting with a grease/solvent lube because that also works well on cables, so it's more of a universal lubricant. But it's dirtier and I'm not convinced I'd want to use it when touring. So I will be carrying both next time I tour.
If you mean "should I carry a chain cleaning kit" the answer is no. Most bike shops will have some way to clean a chain if you really, really need to, and paying for that might even be cheaper than buying a new chain. If you get it caked in mud or something borrow a hose then re-lube it. I rarely use the cleaning machine I have at home, so carrying it on the road is way down the list.