Here is the math on it.
A 13/16 barrel is 812" outside across the flats.
Subtract .540 for this and we get .272
Devide that by 1/2 to get wall thickness and you get .136" (slightly more than 1/8")
Now cut dovetails into it for underlugs. They will be about .045 on the thin side and you then have a wall thickness of 091" under the dovetail slots
That's Less then 1/10 inch.
Now, if your barrel was made of a modern "super steel" like the Chrome-Moly used in a 44 magnum revolver cylinder, it would probably still be safe if it was always loaded correctly.
(You can measuer a 44 magnum cylinder and find that it's not even .091" thick, but it's made of different stuff. A 44 Mag has a top SAMMI pressure spec of 43,400 pounds per square inch, which is far higher than an 80 gr. black powder load would be in a 54 cal with a round ball)
BUT........
No barrel maker would chance it.
You see, any over load, or any air space in the load, could cause problems, and just in the interest of liability, no one is going to do such a thing. It's just not worth the risk.
If you want a very light weight 54 smoothie, get one that's Octagon-to-Round, and get it with a 15/16" breach on it. It could be turned down very light in front of the octagon. You then use solder-on underlugs in the middle and in the front, so you don't have to cut into the thin part of the barrel. Such a barrel is safe, VERY light, and will ballence far better than a smooth 13/16" full octogon.