Can you just clip the bag on the shutters with a clothespin?
Most often I just see the tables with a seasonal type fabric over them...I think you could use that to cover the crate too...unless you were planning on putting your mugs in the crate and not on it.
I saw a lady use a coat/hat rack type pole that had pegs running down the square sides, then things were hanging from the pegs with S hooks.
Sheets of pegboard are often used too, with whatever those metal thingys are to hold products. They are adjustable so that you can hang different sizes on them.

2 pieces of lattice(about 4 ft tall by width of lattice) framed and hinged together so that it stands open and folds for storage makes an easy stand for hanging things too. You could put dolls in plastic bag and hang with big paper clips opened up or Christmas ornament hangers.