Yes it seems like an ideal project for an electronics enthusiast, to turn an old tv into a useful instrument.
A tv already does half of what you need in an oscilloscope.
The other half will be the switches (and rotary gang switches unless you make a substitute), and additional circuitry to get the versatility of operation you need in an oscilloscope.
Then you'll need to add your own knowledge and effort. (A schematic of the tv will help of course)
I think I once saw a website where someone describes doing this project.
To get your signal onscreen, you'll need to:
(1) Locate the vertical deflection circuit. (HIGH voltage! Caution!)
(2) Figure out where you can break the circuit and add your own circuit.
(3) You'll need to locate wires to the vertical deflection plates in the CRT.
(4) Amplify your incoming signal so it measures 50 or 100 or so volts... Without allowing high voltage back to your signal input,
(5) You'll probably need to create two high voltage signals of opposite phase to apply to the vertical deflection plates.
(6) Add whatever amount of DC component is needed to position the beam on the screen,
(7) Cheer triumphantly if it works. Troubleshoot if it doesn't.
The above must be done without ruining any other CRT driver circuits. Basic CRT operation will depend on a lot of things working right. It will be difficult if not impossible to restore basic operation once you've started reworking the innards of the tv.
EDIT: I just found out there are many websites describing how to get this operating in some fashion. You won't necessarily need to amplify the input to as much as 50 or 100 volts. The vertical deflection coils perform this step to some degree