Since the size of the10" hole will be bigger than most fish that anyone here will ever catch, you could probably suffice with a 6"or 8" auger.
One thing to consider is whether you have a hand or power auger. Smaller diameter holes take less time and energy to cut, provided the blades are sharp.
I have a 6" and 8" hand augers and a 10" power auger and I did not use the power auger at all last year even with 2-3' of ice!
I didn't mind the workout which got easier when I got new blades. The only problem was possibly bottoming out.
I hope you are happy and successful with your choice!