|Rotherham key wound and set|
full plate watch, Coventry, 1903.
Swiss watches with gold hands normally have all three gold whereas most English watches such as this Rotherham, which was made in the year that Riddle of the Sands was published, does not.
The same will be found on English cased Waltham watches as most found in the UK are. Plain, rather than filigree, gold hands were I am told rare in America and do not appear in my copy of the Waltham parts catalogue, so it is likely that hands were sourced and fitted locally conforming to English practice, which fits with a common method of selling these watches as described in my post on the standard watch case.
I think it will remain one of life's little mysteries.