In my theater room I have 8 halogen puck lights that are mostly not working and I want to replace them with LED puck lights. On one side of the room I have access to the wiring in the attic. The string of four lights is plugged into the wall with a transformer. This string is then connected to a light switch in the room. On the other side of the room the wiring is buried behind the wall with no access. I assume it's a similar setup. The adapter is a Westek Model Tw60. 120v to 11.5vac. Can I simply replace the halogen puck lights with 12v LED puck lights and leave all of the current wiring in place?
Based on the new power supply picture, the voltage out is AC. This supply may be incompatible with the LEDs, unless the LEDs come with a reverse voltage diode built in.
LEDs have a limited amount of reverse voltage capability: they won't light, but they won't conduct either. However, the reverse voltage is much less than a regular diode, and the LEDs may be destroyed by the AC power supply.
You can get a different power supply putting out 12V DC, then use LED lights compatible with 12V DC (or a 24V power supply and 24V LED lights, but not higher than that.)
If by some chance you can find LED lights that are compatible with an AC supply, then you can proceed.
The position of the outlet with insulation up against the power supply may also be a concern. At least moving the insulation away from the power supply would be a good idea, so the supply can dissipate heat.