That's what I thought, so I had a go at it several times. It was not fun.
The first case I tried was to open the power brick. It is completely glued shut. You will have to slice and saw at the plastic around the seam for a long time to get it to yield, and I did some damage in doing this. When you finally get it open, you find that the power cord is attach at two places that cannot be reached with a soldering iron without additional unsoldering of a lot of components. You may be able to splice the two wires about an inch away from the circuit board.
Then you need to figure out how to put it back together. I used some white epoxy from construction work.
The second case I tried was to splice the cord outside the power brick. The 'tragic flaw' in this approach is that one conductor is spread out into a 100 percent shield of the second conductor, and to effectively shield them again produces a very large bump in the cable that is a lightning rod for later failures. This could be used as a stationary power adapter for a desk.
The third case was to try to replace just the cable-end. The parts are microscopic, including a tiny circuit board with the LEDs on it, and shielding them from each other while soldering them back together is an exercise in self-abuse. The L-shape is much worse than the T-shape, but both are horrible. The cable outer skin is horrendous. Then trying to get them back into the housing is a nightmare.
So what should be an interesting project quickly turns into a 'rite of passage'.