Just my two cents. Expect the temps to be HOT!!! The actual temps won't be too hot, but when you combine a sunny day with the heat reflecting back off of the limestone and the steep and rocky trails, you will drink a lot of water.
Thus, my suggestion would be to go with your original plan of driving over to Dog Canyon. You can reload your water supply over there and the elevation gain is less than either Pine Springs or McKittrick Canyon. If you stay out in the hills too long, you will have to carry a tremendous amount of water. 3/4 to 1 gallon a day per person would be my suggestion. The drive out to Dog Canyon is very nice and Dog Canyon itself is a nice place with few people. The ranger over there is very friendly.
Now if you like bushwhacking, let me know and I can give you some suggestions.

By the way, I love the Wichita Mountains. If you want to get in some good rugged bushwhacking in that will definitely prepare you for the Guadalupe Mountains, bushwhack out to point 1928 in the Charons Garden Wilderness. You will be guaranteed to find zero people and lots of interesting scenery way back in there (take a topo map and know how to use it). If you don't want all that much bushwhacking, climb Twin Rocks, Mt. Lincoln, or Granite Mountain. This are excellent climbs that aren't too far off the beaten path. It is possible you will run into 3rd and 4th class stuff though.
O and at a medium pace, you can do Guadalupe Peak in 4 hours up and back (you'll probably want to add an additional 30 minutes to hang out on the summit). Therefore, a climb of Guadalupe Peak and a drive to Dog Canyon won't be a big deal.