I would NOT recommend a shock collar for barking. Come to think of it, I would not recommend a shock collar to most people as they not properly trained nor used, I would however use it on some people
To get your little barker under control, will take time and consistant training. Just keep in mind you have a dog with two breeds that LOVES to alert you to a leaf moving.
Some simple ideas, a water bottle and a few coins in a plastic 16oz bottle to start with. When your little one barks (and you don't want it) give her a squirt of water. (Make sure it's on stream and not mist, you don't want her to think she's at the salon being cooled.) Give her a shush, too. You can use the plastic bottle the same way, when she barks at the leaf moving, shake the bottle, the noise will catch her off guard and again you can shush her.
These are just a couple of the many good ideas you will get here...hope it helps!