Tom,
Kids are resilient and yours may amaze you with how they handle it. My boys were 13 and 12 when I had my surgery. My wife and I traveled from Maryland to California for my surgery, so they were at home for almost 2 weeks without us. They did great and helped out around the house with the dishwasher, washer, dryer, etc. They were also great when I got back home and looked out for dad while I was on the mend, especially those first few weeks.
Prior to leaving we told them about the surgery, but not in detail, and like others here we tried to not let them see us worry. We did try and answer any questions they had, but again at a high level and not down in the weeds.
Six months later they started doing P90X with me to help keep me motivated, and they still look out for me. Kids are great - they don't care that you are using a straw to draw, that your eye doesn't blink just right, or that you need to take 2 naps a day. They just care that you are back home..
I hope you have a successful surgery and recovery, and I am sure your kids will be a source of strength and inspiration for you.
Ken