What clay are you getting / have you got?
If you're using a clay and a quick detailing spray for lubrication, you can usually get away with wiping away the quick detailing residue with a microfibre cloth as you go - just evaluate how the paintwork is looking when you're done claying and decide whether you think it needs another rinse or another wash.
If it's a bright day and there's the risk of the shampoo solution drying onto the car I wash, then rinse the shampoo off, then clay, then rinse again, then dry using a micro fibre towel.
If it's not too sunny, to save a step, I wash, clay straight after washing without rinsing, then rinse, then dry with a microfibre towel. Or if I'm in a hurry I just wash, rinse, clay and clean up any residue after each panel with a microfibre cloth.
I'm not sure how effective claying is going to be after that all-in-one waterless cleaning product you use, though, as it's a one step product with filler/sealant/wax/magic/whatever in - so if you clay after using that, it's a waste of product cos the clay will take it all off again.
Ideally you want to get all the dirt off without leaving product on the paintwork. Might be best to revert to the traditional (two) bucket, water, car shampoo and mitt method to get the car clean, ready for claying.