While I don't think it's the most practical solution:

The "universal socket" in most stores here is called the Gator Grip. An alternative that's probably made by the same factory much cheaper at Yngfa Trading, $4.75 (US), although the "FOB Taiwan" might bring it up to common US retail prices by the time you add shipping.

The Gator Grip link shows an "adapter" with the hex stud on one end to fit your "electic screwdriver" with the square stud on the other end to fit the socket.

The ratchet mentioned above is on the order of SK Square Drive Thumbwheel Ratchet, also avialable at Sears item #00943410000 Mfr. model #45172, available in 3/8" or 1/4" drive both places.

The one I have came from Sears – I think – and has a 1/4" square stud on one side and a 3/8" stud on the other, but I don't find anything like it anywhere. They must have figured out that they could sell two if they got rid of the flip-over feature.

It should be noted that since these are "mechanic tools" they're heavy and pretty dense, so you might want a separate "carry bag" to avoid putting them in your fiddle case, (should you decide they solve your problem.)

John