The Wessex Wyvern...
Flag of Wessex
The Monarchy of Wessex Coat of Arms does have a Dragon & Wyvern supporter..... as well as a gold "Wyvern" in the crest.
So it appears that the heraldry of the modern Wessex Yeomanry badge is correct albeit I think a Wyvern would be more appropriate and not the Dragon?
The old Wessex Brigade badge is right...
