“I understand how to lose weight, but is there any specific way to ensure that as you lose weight you reduce fat% and not just body mass?”
With a weight loss program there isn’t any way to guarantee you lose only body fat, but you would almost never want this anyway in climbing. Most climbers could do with losing a fair bit of lower body muscle as well.
You minimise the loss of muscle associated with general weight loss by training those muscle groups you need while losing weight on an athlete’s diet.
The only situation you really need worry about loss of muscle is if you diet the unhealthy way i.e. by reducing the proportion of carbohydrate you eat and/or dieting aggressively but then letting it go and putting on fat again.