So he could have been recruited in Australia then, but since he died there will be no way to find that out I assume.
I think it is unlikely that he was recruited in Australia. Although once the war started large numbers of
Australians did fight alongside the British, they arrived mostly as formed Australian units. However it seems that JW joined the KRRC in 1892, well before any hostilities had broken out in South Africa. The British Army didn't actively recruit in Australia at that time, and neither of the KRRC regular battalions had been stationed in Australia - in fact the 1st Battalion was in India through the 1890s, and the 2nd Battalion was in Gibraltar then Malta in the first part of the decade, and then in Natal from 1897.
So I think it much more likely that he made his own way to Britain, either with the intention of joining up, or he joined once he arrived because he couldn't find other work and needed to provide for his family.
Would there be no regimental records that might have this?
Regimental Records tend not to have survived. Any that do will probably be in the
Regimental museum or the Hampshire Record Office. However a quick check of the Hampshire RO holdings doesn't show up anything promising although there are certainly items relating to the KRRC from the relevant period.