Shielding them will be a pain, and pretty expensive to do properly. You can try cutting up a pair of PC speakers, those often give pretty good bang-for-buck.
If your cab is still running jamma, you might have to go to local shops testing. Get a magnetic field sensor app for your phone - anything under about 80uT at the distance from the monitor to the speakers is good.
The problem might be that when you remove the old speakers, you'll find out the tube has been magetised for so long the purity can't be corrected by degaussing. If so, you can try some small disc magnets in the affect corners around the outside of the tube. Or you could leave the original speakers there and try this - you could even start with fridge magnets in this case.