From my own (admittedly limited) experience, it's not the electron beam in the CRT that radiates, it's the electronics all around it.
I verified this years ago with an early Korean clone of the original IBM PC monochome monitor. It was easy to demonstrate: when I turned down the brightness control until the screen went completely dark, the radio interference audible on a HF amateur rig was unchanged. When I instead turned down the *contrast* control until the screen went dark, however, the noise just about disappeared. Why? In this particular monitor, the brightness control simply controlled the DC bias on a CRT grid. It stopped the electron beam, but did not change the RF noise level. That proved conclusively that the noise wasn't coming from the electron beam. Why not, given that the CRT contains the highest video signal levels found in a monitor? Well, if you look at the back of a typical CRT, you will notice that the sides are all coated, inside and out, by conductive paints. These two painted surfaces -- ground on the outside, B+ on the inside -- with the glass between them, form a capacitor that filters the high voltage applied to the tube. (It is vitally important to discharge this capacitor before you poke around inside a monitor or TV!) The inside of the screen must also be conductive, since the electrons hitting it have to go somewhere. So in effect, a CRT already comes with its own RF shielding. On the other hand, the contrast knob was essentially a "video volume control" just ahead of the (relatively high powered) video output amplifier mounted on a daughter board plugged into the base of the CRT, driving its cathode. The radiation came from the unshielded +70V power supply lead into this daughter board. Replacing that one wire with shielded coax and bypassing both ends with capacitors reduced the noise dramatically. I got rid of what little noise was left by adding extra shielding to the monitor's drive cable. I had already tediously painted the inside of the cabinet with conductive paint, but that turned out to be largely a waste of time; the noise level didn't seem to depend much on whether the cabinet was on or off. The bottom line: brute force shielding of an entire monitor is often not required. It pays to figure out exactly where the radiation is coming from, and work directly on the cause. Caveat: this particular monitor, being very old, had no RFI mitigation at all. Almost all newer monitors have much better RFI shielding. Open them up and it will be obvious -- metal shields everywhere, ferrite beads around cables, etc. Simply upgrading to a newer monitor may fix the problem. Phil