Dead ball strike. Hands and arms are not part of the bat but the player has to maintain control of the bat. If the batter makes a swinging motion while trying to elude a pitch it's still a strike. What you describe is more like the ruling if a batted ball hits a player while still in the batters box it's a dead ball. Some of these are very hard to call from behind the plate though.

The secret to a long marriage is to keep on dating, just as you did before marriage. We have "date night" once a week.
Hers is Saturday, mine is Thursday.

The only time a married woman gives those is if your not married to them!