If you simply want to replace the motor with something new, you need to determine what modern frame will fit your machine.
On your motor, there should be a data plate with a frame #, hp rating, etc. Older WT motors have frame numbers which
may not correspond to modern, standardized frame designations. I have one that came off a lathe labeled 118D, whatever that is. Fortunately,
it was close enough to a modern 56 frame motor I was able to use one. It's very possible that a 56 frame will fit your machine.
Here's the information you need:
You need to match shaft diameter and length and mounting bolt configuration. HP is up to you. Since it sounds like you mostly do woodworking,
speed control, while nice, probably isn't necessary. Those older WT machines are excellent: it would be a shame to replace it. The modern
Chinese drill presses aren't build to the same standard.