I still have my 93 KX125, can't convince myself to let it go as it is the strongest KX of any year that I have ridden. Had the same issue with the ignition...was not the CDI or the Stator or the Coil, the resistor in the spark plug cap would open once the motor got warm & lose spark (new coil does not come with the cap). This bike has been VERY reliable with a few details covered, mainly the transfer ports need to be balanced (one side of the cylinders transfers are lower than the other). In my opinion, this is the cause of reported detonation on these motors, the uneven transfers cause a lean condition on one side, leading to the problem.
The 93 model uses a Flat Top Piston with a 16mm pin, if you get a different head you will need a 94 head as it is a flat top (piston 15 mm pin) later years are domed and would need the head cut to accommodate the different domes. Later year rods will fit your crank and offer greater piston selections, just get the proper length rod.
Hope this helps & looking forward to the restoration!
DoldGuy