I believe the point of WBTB is to make you more awake before going back to sleep again making your next sleep more shallow. The most common instruction for what to do during the time awake is to read about lucidity. If I were to exercise during this time, would that be effective also? Or would it just wake up my body and not my mind?
The primary point of WBTB is to get your mind focused on LD’ing, and allow you to fall directly into REM sleep so you can dream. I’ve found that this greatly increases the effectiveness of most induction methods (especially WILD) 
.
As for exercising, I can’t say for sure, but I would think that this would make it difficult to go back to sleep unless it was very light excercise. As you said, the idea of WBTB is to wake your mind, not your body.
However, many people experience more success when they completely wake up during WBTB (ie with a shower, walking outside, etc), so it all depends on the person. Give it a try and see what happens 
I am going to start testing this out in the coming weeks. I plan to jog a mile and do some minor weight lifting (nothing max, only sets of 10 or 12 reps with lighter dumbells).
I’ll either update this thread with my findings or start a new one if any increase in lucid dreams is significant. Right now I am averaging about one lucid dream per week with absolutely no exercise, but I want to use the time awake during WBTB to try and get back into shape.
I also take B6 supliments before bed and sometimes Damiana.
I’ll let you know what I find out.
Well, although this is pretty unrelated to LDing, I don’t recommend doing any type of exercise straight after waking up. I do my weightlifting either after work (early evening) or mid-morning when I am off work. This is straightly my opinion, but I have tried early exercise and it just made me feel sluggish, immobile and unproductive.