Smallest power supply unit

How about 3 AA batteries in a battery holder then?
Get away from the high voltage mains altogether.
Arduino can control transistors to control your lights, does not need much power for that.

I generally just use a wall adapter like this
http://www.dipmicro.com/store/DCA-04510
and put a barrel plug, or screw terminals, on my board it to.

Couple of examples of wall adapter powered boards:
'328 based board


'1284 based board