My300d,
If you get a copy of the "HAYNES" diy manual (w123), they have a very easy to follow section on the axles.
It literally takes longer to jack up the car; remove the wheels and drain the diff., than it does to changes BOTH axles. A trip to the M/B parts counter for a selection of proper width circlips, would be advisable.
I would also advise a bit of anti-seize on the splines on the outboard ends.
I found a pair of axles, for my '81 240D manual, at an import salvage yard for $75.
As a side note: A guy who repairs axles as a biz said that U.S. spec bearings don't last on European axles. So, ask if the rebuilt axles have metric spec bearings. Just my .02 worth.
Good luck, John F.