Acc. to MacColl, Partridge was 90 around 1964, not now, so he certainly could have served in the Boer War.

Otherwise I tend to agree (except for the part about infection being rarer in the late 19th C. than in the 18th; why?).

It wouldn't be especially remarkable for the word "trooper" to have been sung in the Boer War (or earlier). If it meant only "cavalryman" in British English, so be it. All that would have been needed is for one singer along the line to make the change, whether before 1901 or after 1960.

As with most other traditional songs, we don't have enough contemporaneous texts to make a determination one way or the other.