Well, take out the "if" you/we should pass away, I am in complete agreement.
My Dad did what you are thinking: Very accomplished man that wanted zero fanfare beyond family. Cremated, ashes at West Point, no memorial, just us. Mom's ashes with his. For some reason, not sure why, since he never talked about West Point, that was his directive to me.
He didn't want an obit but my sister decided he did. Grave rolling 101.
I am going out the same way. No obit other than my respect for my family, my wife and really great children.
Ashes? Depends on where I will expire: Potomac, American River, Atlantic Ocean. Who knows but it will be water.
Bob got the kids, the kids got Bob. No one else really matters other than family.
Here's looking at you.
Pic I took at West Point. Just us.