New auger bits in old brace

Hello.
I have a few auger bits with hexagonal shafts but my electrical drills do not pack enough power to operate them.
I remembered that I had 2 braces laying around so I decided to use them instead.
You may already have guessed my problem: these old braces have a 2-jaw chuck on them and are designed to work with tapered square shafts and will not grab the new hex shaft.

Do you know of a way to adapt hex shaft auger bits on a 2-jaw brace ?
I know that nowadays they sell braces with 3 jaws for this purpose but I would rather not buy a new full brace (they cost at least 70$) when I have 2 perfectly operational braces as it is (plus one of the 2 was my grand father's so if I could use it more often it would be a good thing)

2 solutions I thought of but could not find anything so far would be to change the chuck only (but where to find a proper chuck, at what price and is the thread even standard ?), or to find a separate chuck mounted on a tapered square shaft that could chuck itself inside the brace's chuck (a chuck in a chuck…).

Any ideas ? When I try to google for this problem, I seem to find only posts explaining how to grind old square-shafted bits to be used in modern drills. I want to do the opposite.

Bonus question, any one knows of a good resource on how to sharpen those old auger bits ?

Cheers,