Luke 17:1 Jesus said to his disciples: "Things that cause people to stumble are bound to come, but woe to anyone through whom they come."
Ideally, it is a dual solution of don't buy the unethical kind, and set up an alternate ethical supply chain to the same region so workers can switch to a better work place.
But, if the latter is not possible, one can at least help decrease the market for unethical cobalt by ceasing purchase.
Plus, it is not a matter of seeming morally superior. If one option is morally better than another, it should be chosen, regardless of the consequences.
So, for instance, if Jesus is correct, that it is immoral to be a path of scandal, then one should choose to not be a path of scandal, even if the state of the world otherwise remains unchanged (e.g. unethical cobalt mining continues).
In the case of rubber the big companies do provide better jobs for the families they employ than anything else, ensure the family gets modern medical care (as opposed to "witch doctor" care anyone not working for them gets), and the children do go to school and so have the ability to get a better job latter. The companies looks the other way in harvest season then families are taking their kids with them to work, so long as the kids are in school. Child labor for sure, but you can honestly argue that the children are better off despite that.
You can decide if you accept that as better or not, but it is a reasonable argument that child labor isn't always the worst possible.
Sadly I don't think in the case of cobalt the above applies.
The idea is that demand for documented cobalt will go up, prices for it will also go up, poorly-documented cobalt producers will have lower demand for their product and their profits will be harmed, the ones capable of fixing their shit so they can sell more-expensive documented cobalt will do so, relieving documented-cobalt supply, and when the dust settles cobalt will be a little more expensive but most of it will be documented.
This is basic policy-building how-to-make-the-world-less-shit using market forces for (old-school) conservatives stuff, and is the backbone of one of the most important & influential strains of political and economic thinking around. It's not remotely radical or unrealistic.