I also used the harness when my daughter got into that stage. I used the one at Target as well. She likes wearing her monkey. Most people realize why your using it and don't give any looks. And if they do give a look, who cares! It's a safety issue. Also, there is a book called HANDS ARE NOT FOR HITTING. It has a page where the child is holding her mom's hand and it says, "Hands are for keeping safe." It's a good discussion book about how to use our hands.
Also when my daughter started this stage we gave her 2 options: hold my hand and walk beside me (even with the harness on), or be in the stroller/cart. Let her know if she doesn't hold your hand at the store and behave, you're going home. Keep it simple with a warning, "Hold my hand or we go home" Follow up quickly with a question, "Do we need to go home?" Usually they grab for your hand because they want to stay. If you head for the door when they don't get with the program, they know you're serious. It certainly is a hard stage that wears at your patience, but eventually they get it if you are consistant. You won't need to leave the store much to get the message though.
If that doesn't work, then say "Hold my hand or no cartoons." And don't let her watch cartoons for the rest of the day no matter how upset she gets. If you give in you send mixed messages and they try to get away with whatever they can. If you're fair but firm they learn the rules you're trying to establish.
I quiz my daughter, "Why do you hold Mommy's hand?" To be safe. Not just about getting lost at stores, but hit by cars in parking lots, etc. Somehow try and work simple safety tips into daily life, and better if you can relate it to a show she watches or book she likes. My daughter actually knows that she has to follow certain rules, but make it fun. My daughter reaches for our hands out of habit now.
Also preface things by saying, "It's Mommy's job to keep you safe, so what do you need to do?" " Hold your hand." "Very good!"
Sing songs you make up about hand holding. My daughter loves it. " We sing "Hot irons are no fun" when my husband irons. So sing about anything, and kids seem to like it.
I also don't let my daughter walk in some stores that are over crowded with carts, such as grocery stores or Costco. Explain why she has to be in the cart for safety reasons.
Good luck! Hope some of my ramble was a help.