No, I didn't. The axle I took out may have been a Wald. It had no ribs. I don't know if that matters. Something in mine had been rubbing and wearing on the axle though. Maybe the axle was bent. Maybe that happens if the bearings are too loose, or maybe those ribs are really supposed to be there. At this point I have no idea. I overhauled gobs of these when I was young, and never thought about any of this. If you needed an axle, you went down to the Schwinn store and bought one, and it fit. There was never a need to give it much thought.
If you are going to buy a Wald axle, I suggest you take piercer_99's advice and look for Wald 294 specifically. I did not see that number in your link. I am convinced some sellers think think these interchange with "normal" 3/8-24 axles, and they don't.
I suspect that might be a real New Departure model D axle in your second link but I just don't know. The one I bought had those 2 sets of marks in the middle (they are raised areas), but it also had 2 more areas like that where the threads end, a total of four raised areas. That made the actual threaded area shorter, leaving no extra threads for adjustment. It really can't be right. I have another axle in the mail. If it is wrong too, I may have to lean on markivpedalpusher after all.
There are no threads in the middle of these, so the disc support sleeve has to come off the end it is closest to. If the threads are hosed, you can make a chasing tap by buying a 3/8-24 grade 8 nut and putting a slice in it perpendicular to the threads. I used a cutting wheel on a dremel tool to slice it. Then if you pry the slice open a little it will thread on the New Departure axle and you can chase the threads with it. That's how I got mine apart. The New Departure axle is 24 threads per inch, just a little bigger than 3/8 so it works.
If the axle is also stretched, you will have to cut it. I had that happen the other day on a Bendix 2 speed. Bendix is true 3/8-24, so the little chaser should have worked on it too. It didn't so I went to a real threading die and discovered that once you got past the bad spot, the die would be trying to cut a thread in the wrong spot, right on top of another thread. No way to fix that, the axle is stretched. I screwed the support on a little further, put a flat washer up against it for protection, and cut the axle off flush with a hacksaw. Then I could unscrew the support.