You should do whatever you feel comfortable with hon.
I will simply speak from experience, as that is all i can do. I did not have shoulder dyscotia with DS1 (amazingly-he was faceup so im actually surprised i didn't get it with him) But i did have it with DS2. So even though mine happened in an opposite order, with SD happening only in my second birth, there is proof that it doesn't always have to happen.
Its hard to say, from an outsider, if c-section is a good route or not. There are so many variables that come into play with shoulder dyscotia. For instance, what position were you pushing in? Was it a medicated birth? Was it an active birth? Did the care provider allow you to choose your position? What was the babys position (face up? hand near face? face down? etc). What manuevers and measures were taken to get the baby unstuck? McRoberts Manuver? All fours? Simply moving the baby's shoulder aside? the Gaskin Manuever, etc? Because if it was related to any of the above, there are things you can do during your next labor to avoid things that can predispose one to shoulder dyscotia or at least decrease the degree of SD, such as not birthing on your back, having an active labor, being "allowed" to push however you feel mother nature wants you to, etc. It isnt a gurantee that it wont happen again, but it certainly could improve the outcome. On top of this, since you have a vaginal birth under your belt now (which you didn't have with your first, obviously) your pelvis and hips have probably changed quite a bit. In fact your pelvic opening is probably larger. So that also will help minimize SD. Who knows, you may get it again, but id be willing to bet if you did it wouldn't be as dramatic as the first. There are degrees of SD. They dont always turn ugly. No one can know ahead of time, how it will play out, but those are things to consider as you approach the birth of your next child.
If it were me, personally, i would probably attempt a vaginal before deciding on CS, however, i think you should follow your mommy instincts. Personally, i will be going for another water HB. Ive had one SD out of two, so there is still a chance it wont happen again. If you feel a CS would be in the best interest, that is understandable.
PS that is interesting about the baby crying. Mine didn't cry right away either...the silence was very ominous.