I think the clue is in the expression “…one of the Zulu wars.”
The 6th Inniskilling Dragoons arrived in South Africa in 1881.
Their first involvement with AmaZulu was to provide the escort to King Cetshwayo on his restoration in January 1883.
Elements of the regiment were involved in evacuating refugees from Zibhebhu’s forces in 1883 during the civil war.
In 1888 the Inniskilling Dragoons, together with the Inniskilling Fusiliers along with other British and Colonial forces were deployed against the rebels of the uSuthu faction. The “Skins” were present at the following actions: the Battle of Ceza, 2nd June 1888 and the Battle of Hlophekhulu, 2nd July 1888.
The regiment were involved in pacification operations in KwaZulu until September 1888.
I have the Blue Book relating the 1888 campaign.