I'm a bit older, so my problem was what to tell the grandchildren. I remember how relieved my 11-year-old (at that time) granddaughter was when I sat down with her and explained what was going on, that I was going to have surgery, and that the outlook was good.
Kids are pretty perceptive, and she knew something was wrong with Grandpa, but no one would talk about it. She definitely appreciated being talked to like a young adult and felt a whole lot better after our conversation.
The rest of the grandkids are much younger and didn't really know what was going on.
I don't know how old your children are. That's definitely a consideration, but kids are pretty resilient. Sure, they'll worry, but they may surprise you with their reaction to the news.