It's weird that you know enough about the CRT to know how to adjust geometry with magnets, but not enough to know the way the voltage is stored. CRT repair is dangerous - you should understand how the CRT works - not just follow step by step instructions. This is true not just for safety but also because these are finicky analog devices that don't always respond the way the book says they should.
The short answer is that yes, the outside of the tube itself is perfectly safe. But that is not really enough to know, because you can still zap yourself.
There are two kinds of high voltage danger inside a CRT. First, the power supply, which can easily contain 200V or possibly up to 800V. Second, the tube itself, which can contain 25,000 (yes thousand) volts or even more in a large TV. The voltage in the tube is proportional to the size of the tube, about 1KV per diagonal inch, give or take. The power supply voltage can burn you and knock you down, the tube voltage can kill you. Most of the power supply voltage will discharge on its own given a few hours or days, though - especially if you unplug the CRT without turning it off, just like a PC power supply. You should still discharge any large capacitors safely before you handle them.
Voltage in the power supply is more likely to zap you because it's more exposed, but the danger from it is less. The tube voltage is by no means safe. If you look inside the case, you should see a large wire connecting the tube to a bulky component which is the flyback transformer. The tube end of the wire attaches to a "suction cup." It isn't really, it's actually an insulator, but it looks like one. This wire, the transformer, and sometimes some other components are all at high voltage.
It isn't always necessary to discharge the tube before working on the CRT. In fact, many adjustments can only be made with the case open and the display turned ON. Any activity inside the case when the tube is potentially charged should always be done using an insulated tool, wearing insulating gloves, no jewelry, no dangling hair or clothes, and with one hand in your pocket or behind your back. This will at least hopefully keep the current from stopping your heart if you manage to zap yourself.
To discharge the tube - which you should do before replacing any components - you connect a wire to a screwdriver, the other end of the wire to the chassis ground (NOT earth ground or electronic ground) and poke the screwdriver under the cap until it touches the terminal. Wait a few minutes, then go back and do it again. Remove the cap (it has clips under it which you can squeeze to release) and connect the ground wire to the terminal.
If you have any safety concern whatsoever, it's best to find someone who is willing to do this for you. There may not be any CRT repair shops still around, but there are still some people around who worked in them and remember how to do things. Safety is more important than color quality!
Edit to add: Most of what I wrote applies only to repairs or adjustments you might make with the CRT disconnected from power. If you decide for some reason to work on it with it turned on - which you probably will once you start fiddling with the picture quality - you need some additional safety precautions. The power supply voltage can kill you too if it's connected to mains electricity, and a few CRTs have a "hot chassis" - the whole metal frame is live! Needless to say this is very much not perfectly safe to touch. Because of these and similar issues you need an isolation transformer - with isolated ground - to work on a plugged in CRT. This will allow the CRT's voltages to float independently of the external environment, so you can connect things like oscilloscope probes and your fingers without trying to discharge the whole power supply through them.