I used the DD bells for the first 2 years of my comp training. I will guess my hands are smaller than yours. No, I couldn't get my thumb and index finger to meet. The best that I could do is maintain a "C" grip. Not a crush grip, just enough to hold the bells. I could still manage 200 reps with a DD 16kg (one switch). So, it's nice to have a smaller handle, but you can get by without it.
The comp bells have handles 33-35mm. Actually with the 35mm, I cannot get this finger lock or maintain it.
Men who do Jerks with the 32s use squat jumps as an assistance exercise. It is actually only to a depth that closely mimics the first dip/bump of the jerk. It sounds like what you are doing. I haven't found a need to do them yet, but I only do work with the 16s and 20s for double jerks right now. But, yes, what you are saying definitely makes sense. Typically, these are a supplemental exercise performed for 40-50 reps (sometimes with as much as 300lbs depending on the athlete). My guess is that if you are doing them before it is priming you well for the first bump. What has worked for me in the past, is jumping rope. But, a set of 15 won't kill you or your legs from the sound of it.