The Hands are NOT part of the bat

It IS black and white.

A bat doesn't have hands.

1.10

a) The bat shall be a smooth, round stick not more than [varies] inches in diameter at the thickest part and not more than [varies] inches in length. The bat shall be one piece of solid wood [or other approved material in amateur ball]

Note the lack of hands in the description.

The hands are part of the batter.

2.00 The PERSON of a player or an umpire is any part of his body, his clothing or his equipment.

As for when what happens:

2.00 A STRIKE is a legal pitch when so called by the umpire, which:

e) Touches the batter as he strikes at it;

f) Touches the batter in flight in the strike zone

6.05 A batter is out when_

f) He attempts to hit a third strike and the ball touches him;

6.08 The batter becomes a runner and is entitled to first base without liability to be put out (provided he advances to and touches first base) when_

b) He is touched by a pitched ball which he is not attempting to hit unless

1) The ball is in the strike zone when it touches the batter, or

2) The batter makes no attempt to avoid being touched by the ball; If the ball is in the strike zone when it touches the batter, it shall be called a strike, whether or not the batter tries to avoid the ball. If the ball is outside the strike zone when it touches the batter, it shall be called a ball if he makes no attempt to avoid being touched.

APPROVED RULING: When the batter is touched by a pitched ball which does not entitle him to first base, the ball is dead and no runner may advance.