Skipping is a very effective mode of cardio, next to running IMO for working your entire body. I personally do a lot of skipping (see my Training/Supplementation logs). I rarely skip more than ~20 minutes, and I almost always do it HIIT (i.e. with efforts and rest intervals). It's definitely effective for fat loss (provided your DIET AND THE REST OF YOUR TRAINING is on point).
Also, if you have "shin splints" - this is a very broad term that covers a variety of injuries related to the lower leg, including but not limited to medial tibial stress syndrome, compartment syndrome, etc. - then I highly recommend that you:
a. Find out what it is that you have specifically, and
b. Start rehabbing your injury.
If you want to switch things up re cardio then you can also use the following options (they won't stress your lower legs):
* Cycling (or stationary cycle)