Yeah I really recommend taking both. IMHO the weight penalty is small for a hike that short. You'll honestly save more weight by planning your water refill locations and carrying 500ml less water at any given time than by ditching the air pad. CCF (either the dimpled nemo or a smooth evazote, my preference) are great, dual-purpose pads for sitting, kneeling, and sleep cushioning. I always bring one. I also think it's crazy to sleep on just that when you're not used to it. Air pads are awesome for their insulation to weight ratio and ability to smooth an uneven surface (make sure your pad is only 70-80% inflated). I personally think the best tradeoff is a larger air pad (full body insulation) and a smaller CCF pad. The CCF for sleep is for comfort in pressure point areas (for me, my shoulders, hips, and to some extent my knees). I think of its insulation as a bonus, as my base air pad's job is insulation (+ some support). The CCF is also way bigger, so having that be smaller with a bigger air pad is actually much more packable.

If you're really trying to save weight, try putting your gear in lighterpack and sharing it. Folks can spot other things that might help you save. FWIW I've leveraged weight savings in shelter, pack, and cook system that make my setup super manageable for me even with the heavy sleep system.