both Canada and Australia (and perhaps other I can't find) have military uniforms and/or insignias to be worn by their governor-general in their capacity as de jure commander in chief of the armed forces.
The Governor/lieutenant governor however do not/ Obviously, this comes from the fact that unlike the federal counterpart, they have no official place within the army hierarchy though they are often present in some capacity in state/provincial unit's functions to lend their royal patronage.
It occurs to me though that many state/provinces have organisation that depend solely from their level of government like, say, the New south wales state emergency services or the Ontario Provincial Police and that having some all purpose badge could be use during function to represent their patronage of said organisation. In canada there is currently a badge used by the Lieutenant governors but it is the same for all 10 and while the COA would seem a good choice, those (by themselves or in a wreath) are used by the respective Aide-de-camps so something else would have to be chosen.
Another thing is that although the governors/lieutenant-governors have the windsor uniform, it is rarely worn these days probably as it look overly anachronistic. Judith Guichon and Iona Campagnolo of British Columbia both tried to modernise it a bit but I feel more could be done, maybe using local symbols, colours or clothes to make it look a bit more relevant.
No idea yet on my part but just thought I'd share until I come u with something. feel free to contribute.