Sorry ... My lights have a cord and plug and are not truly cordless.
Almost of my clients install a recessed outlet directly behind the artwork to hide the cord and my lights have special plugs to fit into these outlets so the artwork will fit flush with the wall.
The Best Recessed Clock Outlet is the Leviton 688 (one single outlet) or Leviton 689 (dual outlets). Available online or at HomeDepot and various hardware stores. They cost around than $10.00 or less and can be installed with little effort.
A good reasonable electrician should be able to install them in less than an hour and should be able to installed without having to patch or repaint.
Most of the time there is an outlet below your art and can be wired up from the outlet below.
It is not necessary to have them wired to a switch as my lights have a build in dimmer and on/off switch.
I get lots of inquires about building a quality cordless battery powered picture light, however I must admit I get more requests to replace them.
Battery Picture lights come in a number of varieties, Incandescent (flashlight style) or fluorescent (camp light style) and the newer LED.
My clients replace the cheap ones all the time due to the fact that they don't light the painting very even and some only light the top 4 or 6 inches.
There is a new "High Priced" LED on the market that offers "this high-capacity battery pack will allow you to run a 24 inch light for up to 5 hours"
It's a $ 175.00 option (more than the cost to install a recessed clock outlet) and you have to unplug it and recharge it after 5 hours?????
If you own one or purchase one, try this test.
Invite a few friends for dinner, turn on your battery powered light when the doorbell rings, uncork a good bottle of wine and put the dinner on the table, before desert check to see if your battery powered light is still running. There is a good chance it won't make it till you guests leave.
Take a little advice. Use a recessed outlet behind the painting, and enjoy desert.