I'll most likely cut the plug and run it through the wall into the closet to a light switch. There's one there for closet light already.You could use Museum Putty (transparent, removable) instead of melted wax.
For a 2-conductor wire, you can buy an inline cord switch. (You cut the cord, then attach the wiring inside the switch.) For a 3-conductor wire, there are switches already wired, with a plug and socket on short cords.
I like the very white light bulbs you're using!