Can I power a german 240v spindle motor off of a USA 240v nema5-50 welder plug?

Nope, you must put a 240V 15A plug on the cord. (NEMA 6-15).

Then, install a 15A/240V circuit with NEMA 6-15 receptacle(s)...
or a 20A/240V circuit with NEMA 6-20 receptacle(s) (which will accept 6-15)...
or a 20A/240V circuit with 2 or more NEMA 6-15 sockets (e.g. duplex recep).

Trying to re-task that 50A welder circuit to serve that purpose will be much more trouble than it is worth, and would be a one-way operation (meaning you could not plug 50A appliances into it anymore). Just run a new circuit.

You could look at fitting a 240V-only subpanel where the welder socket now is. You can put any number of 240V-only circuits ranging from 15A to 50A. (you cannot use more than 50A of them at one time obviously)>

• However you must be careful not to put any 120V circuits in it. I strongly disrecommend using the subpanel's neutral bar for a ground bar. I recommend isolating the neutral bar (remove neutral-ground strap or screw), hook nothing to it, and add an accessory ground bar ($5) for all grounds. That will warn "the next guy" that 120V loads do not belong here. If someone hooks up a 120V load anyway, it won't work, and troubleshooting will soon expose that no neutral feeder is present.
• One notable problem with 240V-only panels is it is difficult to run AFCIs or GFCIs out of them. They need 120V to power themselves (their own detection circuits). This is relevant because as of NEC 2020, 240V circuits must be GFCI.