CRT monitors, as opposed to hard disks, are quite sensitive to magnetic fields.
Except for my old 17" Nec Multisync 5FG, just to gain access to the electronics you need to remove kilograms of shielding....
It's bigger and deeper than my actual 22" Iiyama...(but then except the CRT tube...)
As Cathar said, don't worry about your HDD...
CD