Switching a 240 volt 3 wire to a 250 v 2wire

I believe the question that Nate wants to ask is along the lines of "What do I do with a neutral on a 240v / nema-6 style plug?" I'm going to assume that you are on an American-like single phase 120/240v circuit, as you are talking about 'X' (black?) and 'Y' (Red?) while not mentioning a neutral on the old welder. The term X and Y are used for multiphase electrical, but for simplicity I'll continue using it to refer to the two wires that make up the 240v circuit.

Your welder should be on a circuit completely independent of the rest of the plugs in your shop, assuming that you have the one 250v 60 amp plug. If you simply cap off the old wires with a twist-on connector, and keep the breaker in the off position it shouldn't interfere with any other plugs in your shop.

For the generator, the way you explain it having 'three wires' I'm suspecting that there is an 'X', a 'Y', and the neutral. The neutral is likely centre tapped to the transformer, so if the welder requires only 'X' and 'Y' you can safely cap off the neutral wire with a twist-on connector. You won't need the neutral unless you need a 'four pinned' connector in the future, or you want to install 120v plugs.

Do not modify your generator!

You need to make a short adapter cable.

Your generator surely has a NEMA 14-20 or NEMA 14-30 socket. Identify which one it is (post a pic and we can help).

Your generator surely has a NEMA 6-50 plug, but confirm that (ditto).

So you need an adapter cable with the reverse: a NEMA 14-xx plug and a NEMA 6-yy socket.

You can go online and somebody will sell it to you. Those generally fall into 2 categories: Bubba in West Virginia builds them to order out of quality parts from the electrical supply house, or the Chinese make them on their fancy injection molder, but they're rubbish.

Or you can step into Bubba's shoes and build your own, with parts from a proper electricacompetent electrical supply house (NOT big-box), and buy three things:

• A NEMA 14-xx plug, with xx matching the size of your generator's socket.
• 2 feet of #12/3 or #10/3 cordage. This will be black white green. The size matches the xx size of your plug: 20=#12 30=#10.
• An inline NEMA 6-50 socket made for cordage.

Get em together at a real electrical supply, and the competent clerk will make sure the strain reliefs fit the cordage... do not use scrap Romex for the cordage, it won't fit the screws or the strain relief. It's only a couple bucks to do a proper job of it and have an adapter that will last.