A bit suscinct but this is correct. Years ago I did exactly what you propose for a friend's old Raleigh since we couldn't find suitable cups with Raleigh's proprietary threading. I just exchanged the cottered Stronglight spindle for a proper length SR square taper spindle and crank and kept the old Stronglight cups. I did use new bearing balls.

The required axle length is determined by the crank you use and must be long enough so the chainrings don't hit the frame but not so long as to give a poor chainline. Square taper axles will usually be shorter than a cottered axle.