If there is illegal contact using the hands away from the ball, it is advisable to not use the term "hand checking". It is a foul, regardless of what term and signal you use.
Coaches now have come to equate "hand checking" to action on the ball handler. Therefore, it is a good idea to use either a hold or a push or even a hack (we don't use illegal use of hands in Texas
) when reporting your foul. There is no difference in the penalty, so why try to confuse and incite the coaches over semantics.
The same thing goes for a drive to the basket. If there is a shot taken, the call should be something besides "hand checking".