Does the transformet appear to be designed be able to have a different power cable, like NM, installed?
You also might try using a 'clock receptacle' above the cabinet. It has a single outlet which is recessed a half inch or so from the wall surface. If the box is mounted horizontally close to the top of the cabinet, it should minimize its visibility.

No, the transformer has [lamp] cord coming out of it.

Who designs this stuff?

"the "cord" goes into the wall and enters the box with the receptacle, not through a knock out but through the mounting holes in the side of the box.

"the transformer has [lamp] cord coming out of it."

Is their a plug on the end?
'zip cord' is not rated for use in concealed locations, and inside the wall is concealed.

Yes, I know zip cord isn't approved for concealed locations. No plug on the end. I suspect the original installer just cut off the plug and connected the cord directly to the switch.

I'd really prefer not to put a receptacle above the cabinet and was hoping for other ideas. Although I'm not sure one exists.

It's beyond me why they would design something like this (beyond the obvious, "make it as cheaply as possible).

If he mounted the cabinet in such a way that you don't need any tools to take it out (such as with a screw through a keyhole slot), would he be allowed to put the clock receptacle behind the cabinet, providing that the wire is passed through a hole big enough and protected with a rubber grommet? If allowed, he would just have to buy a plug that's 90 degrees offset, so it would not protrude from the wall and touch the back of the cabinet.

Here is a link that might be useful: 90 degree plug

Put a receptacle in the cabinets or a clock type receptacle behind the light.