I've no reason to doubt that Richardson was wounded on 6 January 1900 but just not at Wagon Hill. Units were deployed at other points on the perimeter to counter Boer diversionary attacks and these included the Leicesters, Gloucesters, Liverpools and even some of the Devons.
British histories tend to ignore this aspect of the 6 January operations but Deneys Reitz was there as he describes in his book "Commando". 400 men of the Pretoria Commando plus his unit of Free Staters set off from Bell's Kopje in a diversionary attack on the northern perimeter defences and in particular a feature he calls the Red Fort. The Boers appear to have come off worse suffering a number of casualties. Richardson must have been one of the British casualties of this action.
Although not a Wagon Hill casualty Richardson was a scarce casualty of the attack on the perimeter line. I certainly don't recall seeing a QSA to one on the market before.