These dimmers when at their full on position will be with a fraction of a percent of full brightness. You need not worry about that.

As for damaging the LEDs, no that's not going to happen either. Regular (non-halogen) incandescent bulbs will last longer at lower brightnesses and halogens will not get the benefit of the longer life through the halogen cycle if you don't run them hot enough, but CF and LEDs are not going to exhibit these issues.

Thanks. You've given me some peace of mind. I wish, I wish, I wish I would have asked the furniture builder more questions before he put all this in, and I would gladly have coordinated with and electrician, who came out before the install anyway to add lighting to the room.

It's much more complicated now since the furniture is "built in" and doesn't really move away from the wall. It'd have to be taken apart.

Oooh, I forgot to ask. The lights plug into a transformer, which then has a cord that goes to the outlet. Still OK?

The worst thing that will happen is the lights won't dim typically. If the transformer and the dimmer are compatible they might dim properly. Again, you need not worry much.

You could just get an extension cord and an inline switch.. .here's an example but I've pretty sure I've seen them at the home center.

If not you can add a switch to like this to any zip cord extension cord...
inline switch

Here is a link that might be useful: switched extension cord

Thank you! The switched extension cord is exactly what I'm looking for.