If the original CRT TV was in a cabinet, you could install a vertical wood brace from the bottom of the cabinet to the top. An articulating mount can be used for the new screen to allow the screen to be pulled out for viewing.
If the original CRT TV was on a shelf, the new screen can be placed with it's included desk stand onto the same shelf and straps can be used to secure it for travel or it can be removed to be placed on a mattress.
I have a 32" screen on an articulating mount. The mounting bracket is fastened to a 5/8" plywood strip (about 6" H) that spans three studs. The plywood is glued and screwed into the studs. The articulating mount is strong enough so that I don't make any extra efforts to secure the screen. If I was traveling to Alaska, I would install a strap to secure the screen.