*probpt: well as far as i know if you just apply Nano systematic care you don't need to cure it that long you should give it only about 1 to 2 hours, only the Long life sealant needs to be cured for a minimum of 12 hours but preferably 24 hours, there were some instances in my case that hazing could occur when cured 12 hours and below.
Next that would depend on which Collinite you would be using? 845? 476? 915? If you plan on layering these waxes, which is recommended since you haven't really applied a long lasting LSP like Long Life Sealant. Then layering waxes would be a nice way to go. Sadly 845 based on experience doesn't have that much difference when layered, only Collinites paste waxes have a significant advantage when layered which are 476 and 915.
With regards to your question, it would be always best to wash the car since you already drove it outside, why? because when you drive your car outside even if it still looks clean, dirt particles may already be lodged to the paint cause of the speed of the vehicle traveling and hitting dusts, this not only sits on the paint but in some cases takes more than QD to remove and since you would be waxing, pressure while waxing might dislodge these particles and cause swirls. Another reason to wash your car would be because of the oily films cars get during traffic.
One more thing is because if you use QD's, some QD's (not all) contains nourishing oils and polymers and this might cause a problem with the wax properly sticking/bonding on the paint.
When i layer waxes (not sealants) i always wait for 8 hours to fully cure, then i just use a duster or MF towel and then gently glide them over the paint to remove the dusts accumulated within those 8 hours before i put on another coating, the same can be said about the Nano systematic care, actually sometimes i just put on the NSC and then wait for 1 hour before i remove it and wait another hour or two to cure it and then i go directly to waxing already.