No, you don't
need to strip the wax first but you may get better results if you do. A very quick once over with the clay bar again will strip the wax with very little effort - it's faster and easier than using a paint cleaner or a Dawn wash. I just did this to one of my cars a couple of weeks ago. I would suggest you go lightly with the Cali Duster and follow up with a quick detail spray to clean ALL the dust off before doing the clay again.
When applying the #7 make sure to work in areas no bigger than about 2' x 2', work it against the paint and wipe it off while still wet. Follow that immediately with your coat of, I assume, #26 Hi-Tech Yellow Wax. Put that #26 on nice and thin and let it dry for about 20 minutes before wiping it off. Put a second thin coat on just to ensure even coverage and appearance.
For what it's worth, I'm a Surface Care Specialist at Meguiar's in Irvine, CA. Just so you know I'm not making this up as I go along.