A "Concede Putt" button and "Concede Hole" button are redundant. If I concede my opponent's putt for a par, and I have a putt for a bogey, then my concession would give my opponent a par and the win for the hole. No need to concede both the hole and the stroke.
In the example above regarding Kiawah 17: Player A hits two balls into the water on Kiawah 17, and Player B hits it on the fringe. Player A hits his next shot (his 5th) onto the green, and the best he can score is a 6. Player A would then concede Player B their next shot. Player A loses the hole with a 6 to Player B's 2, and they move on.
I do think that there should be a "Good-Good" button for situations where both players have short putts to halve the hole. I'm willing to concede your putt only if you're willing to concede my putt. If we mutually concede, the hole is halved and we move on. If one person wants to make the other putt, that is their prerogative. This is the way match play works on a real golf course.