In short, no you can't use magnets to fix. Most magnets are not strong enough to affect the "stuck" magetism on the frame or on the shadow mask caused by speakers. If you break a speaker apart or take a hard drive apart, you can find some REALLY strong magnets (yes, in a hard drive--they're amazingly strong). My experience has been that while I can use hard drive magnets or a large speaker maget to degauss, it generally doesn't "stick". The old magnetic field comes back. Or worse, unless you know how to align them just right, you can make the problem worse, not better.
The best thing to do is buy or build a degaussing coil. You can build one out of parts from a dead computer monitor or television--Plus a light bulb socket, light bulb and momentary contact switch and some AC wiring. Check out oscarcontrols.com for info.
However... do you have a 150 watt "gun" shapped soldering iron? If not, go to Harbor Freight Tools and buy one for $6 on sale. These can be used as an pretty good replacement for a degaussing coil.
Also "sticking" a magnet in the case will probably rebend the signal over time causing the opposite color to appear (purple vs green typically).