I recall having a related discussion about this at a clinic a while back. I had an impacted wax problem due to an overly enthusiastic shower can you believe! I have the more normal (for Europe) wet cerumen (wax) type. We were chatting while the the nurse went for the water pulse thing and I asked if this was a common thing to which he replied, perhaps more with the dry earwax rather than the dry, explaining the difference.
I asked about how the variation came about (I do these things) and he said he didn't know why so much as how - it is due to a single switch in the ATP-binding cassette C11 gene (I had to look the name up again - all could recall was C11 and cassette). The gene switch was identified by Japanese scientists quite recently he said.
The single mutation is one where a G (guanine) molecule is replaced with an A (adenine) molecule in the DNA. Those inheriting a version of the 'A' gene from both parents have dry earwax. Those who carry two 'G' versions, or one 'G' and one 'A', are destined to live with wet earwax. So I suppose if an Inuit married a South African they'd be more likely to have wet wax children, who'd sweat a lot.
Over 95% of those with European and African ancestry have the wet wax and about the same (80-95%) of East Asians the dry (for South Asians, those from the Pacific, Native North Americans etc it's about 30-50%). If we did all come from Africa, it seems likely that the 'original' form was the wet.
It's thus likely that the dry form came later, and was carried across the bering straight from Siberia, perhaps 15,000 years ago. With it's ubiquity in Native Americans this seems plausible, especially when combined with other genetic evidence.
The Japanese scientists went on to suggest, (as did you) that the Gene's role in sweating was a factor that ensured it's prevalence among those in primarily cold climates where sweating isn't advantageous. Those in Africa and Europe where it is, tend to sweat more and have more pronounced body odour than those in East Asia. They disagree with you on that to some degree in the sense the sweating modification may have been cause enough. Perhaps as you suggest, a disease or other cause could have caused a fortuitous mutation, which being useful, was perpetuated. It's all but impossible to be certain
As was asked by Sr R, it's not considered that ear wax or its type plays other than a very minor role in fitness, merely forming a barrier to dust and bugs, though it does have anti-bacterial properties. The variation of type coming only as a side effect of the mutation of the C11 Gene, itself brought about for other reasons.
Completely off topic but fascinating none the less.