Normally it is just fine to swap only the tube, and keep the electronics (chassis board).
The arcade chassis are preferred since they are streamlined (no tuner and audio circuits etc) and built to be powered on 24/7 (well, at least the more expensive ones).
Usually you also have a lot of different settings that can be tweaked with potentiometers for all kind of geometry and frequencies so that you can get a perfect picture for every game.
A standard TV is set for one very specific resolution and frequency, and usually there is only minor changes you can do. Some have more advanced settings in the “service mode”, but then you need that secret service code and the remote controller to enter it.
Not all arcade chassis can be used with all tubes. There are different number of pins and configuration on the neck boards, and also different voltages (depending on the size of the tube etc). But if you know what you do, it is perfectly fine to swap an old tube with one from a standard TV and keep your game running for many years to come.
And once again, the Trinitron design is different (Google if you want details ) so here you must keep the TV chassis and replace the one you have today.
My experience is that if you go with a standard TV chassi you don’t need to mess around with the color settings, since all that is perfectly tuned already. The biggest problem is to adjust the screen size and position for some games, depending on resolution an frequencies.
Couldn’t tell from you profile were you live, but if you are in Europe and you have an RGB Scart it is very convenient to hook it up.
Sorry I can’t help regarding the physical size and if it will fit or not. What I can tell you is this – make sure you get help when doing it.
An extra pair of hands is more or less a must, supporting the weight and to be able to mount nuts and bolts conveniently.