Thanks, HillRider. The axle that's on there now is only about 3mm on each side, so width + 6mm. Sheldon suggests that that's adequate esp. if you have a 120mm originally, and pop it out to 126mm, so as to use the original axle. Not sure why you'd want to use the original axle, but Sheldon said it could be done. Frankly, though, I want to have the extra 2.5-3mm so that the seating is ample.
Not that axle wear matters: this is a 41 YO bike and I don't expect to be here when it hits 82. But should be nice to know it's well set up for whomever rides it in the future.
Next step, after the wheels, is to clean up the frame and parts, and to install new cables and housings. I'd repaint it, but it has a really cool League of American Wheelmen sticker on the frame. Too interesting to paint over!