I can't see the point in keeping this from your children. The more people know about cancer and the more people they see cured of it the better. 50% of people in a first world country will live long enough to get cancer, so we as a society should get used to it.
Anyway, surgery is not something you are likely to be able to hide. A few days in hospital, a few months of cautious lifting and carrying things, possible incontinence for a few months or occasionally life.
EBRT if you can hide four to six weeks of daily hospital visits, possibly fatigue and some unusual toilet habits, weight gain if hormone therapy required.
I don't know enough about seeds, a day or two in hospital otherwise presumably the same effects as EBRT. So probably something you could hide.
The search function on this site is awful, but if you can find posts by "johntheprint" you will get info on seeds and recovery.
Not too sure how the family conversation will go if you have any complications, and the children ask why you were keeping secrets from them.