Original Civil War Corps Badges are somewhat rare - some are fantasies.
The badge for Wilson's Cavalry Corps was never ordered, nor made during wartime - merely 'proposed' - the only illustrations being the drawing above and a very similar smaller version.
The 'carbine' was to be a Sharps, since that was the original weapon - but that term came to mean 'Spencer' as well.
Long after the War was the heyday of the Grand Army of the Republic, and to a lesser degree - the United Confederate Veterans - both organizations who would become powerful political forces in their respective areas.
At that time was born the 'Veteran's Badge' - sometimes a shield, other times a 'ladder' - and these were purchased at the Conventions by proud veterans who could have their unit designation emblazoned on them, as well as their names and dates of service.
Any badge for an outfit like Wilson's Cavalry Corps was likely jeweler-made during the post-war era - and they'd be beyond rare, since they would've been expensive at the time, and were probably given as a gift to a senior Officer.
Look at a copy of 'Civil War Corps Badges and Other Related Awards, Badges and Medals of the Period' - by Phillips.
In it, you'll see original examples, period advertisments and fakes.
That being said - if you're being authentic to the time frame, you'd wear a society badge on your dress uniform - but not on a campaign uniform.
Vaya,
Scouts Out!