You can try quieting it down. If it's a DC fan, clean the blades well. Look under the label, you will likely find a small plug. Remove it and drop two drops of 3-in-1 Oil in there. Replace the cap and clean the outside. Put some tape over it.
If it's an AC fan, it's a little more complicated, but it also involves lubing it up.
Do me a favor and tell me what kind of monitor you have in there, make and model
I just got a KI2 that is missing the chassis.
Post a picture of the BACK of the tube in Monitor/Video. Should be able to ID it from the PCB mount.