To the right of your post, I saw a link to the Vidalia Chop Wizard (ChopWizard.com). It looks really interesting.

I've used the old version of the slap choppers, not the newer ones. They worked, but they were more exercise than using a knife (it took a lot more than 8 slaps to chop anything).

I've used my food processor and my Rocket Blender (like the Magic Bullet and other personal blenders) with good results. I've made salsa, hummus, gazpacho, ham and chicken salad, right in the blender cup. It works well for sorbet too (frozen fruit and some type of liquid, I like to use Diet Sprite or lemonade, but even water will do. You can sweeten if you want to, but with frozen strawberries and diet lemonade or soda, there's no need (in my opinion). You can also make a really good "ice cream" with only frozen bananas and nothing else (or with a tiny bit of milk or water to make the pureeing easier). I know that's not a salad, but I get carried away with Rocket Blender recipes. I love mine.

A lot of times I'll just use a knife and cutting board, but I'll make enough sliced vegetables for three or four days of salads, so I only have to do the chopping once (I do that with the other types of slicers and choppers too. Because cleaning the device is often a pain, it makes sense to do a few days worth of veggies at a time).

Food processor, or find a knife skills class at your local kitchen/cooking store or maybe community college. Chopping is a lot less hassle when you, well, know how to do it efficiently and quickly, and it's very much a learned skill.

Knife skills are great to have, but using a chopper is invaluable for onions to avoid irritation to the eyes when dicing/chopping.

I don't know the specific slap chopper you're referring to, but I have an Oxo Good Grips onion chopper that works very well. It's inexpensive and I couldn't recommend it more.