It may be best to transfer as much as possible with the CRT - yoke and purity and convergence magnets. The connectors to the yoke may need to be changed but this may be the least of your problems. Difference in yoke impedance and other characteristics may result in anything from incorrect size to a truly spectacular melt-down! The latter is much more likely with SVGA monitors compared to similar size/deflection angle TVs.
Where the neck size is the same, the yoke can be moved from one CRT to the other but you will have to do a complete purity and convergence set up and even then you may have uncorrectable convergence errors. See the section: Swapping of deflection yokes.
(From: J. G. Simpson (email@example.com).)
Monitors are generally designed by choosing a CRT, then the EHT, then designing a yoke to scan the CRT, then designing a driver circuit to drive the yoke.
In a CRT test lab it's common to have variable supplies for EHT and other voltages, a small selection of yokes, and variable amplitude drive circuits.
EHT affects scan sensitivity, brightness, spot size. You can't get high brightness and small spot size on a large monitor with 3 kV of EHT. Virtually every variable has some effect on convergence. Spot size is important, in as much as you want most of it on the phosphor and not the shadow mask.
Provided the neck size is the same you can swap tubes in yokes but don't expect it to work very well. Different tube manufacturers may use radically different gun structures. A given yoke and its driver may give underscan or overscan and it's pretty well certain that convergence will be way off.
The military spends a small fortune on trying to get the drop into the yoke and it flies with no adjustment or convergence CRT. For the rest of us swapping a CRT is a pain in the butt.