In these breakaway situations, as well as when forechecking, backchecking, and skating without the puck, it is often preferable to skate holding the hockey stick in just the top hand.  This allows for maximum skating speed, and encourages the proper use of the arms (forward/backward, not side to side).  Keeping two hands on the stick forces players into the habit of keeping the stick off the ice and swinging their arms from side to side.  I call this side to side motion "cradling the baby".  Don't cradle the baby while you skate.

A famous NHL player once said, "A player who carries the stick in the air is playing for the other team."

Why?  If the stick is in the air you often can't get the stick down quickly enough to take a pass. This happens all too frequently, even at the NHL level.

Another famous NHL player once commented, "I'll never pass to a teammate who has his stick in the air - I don't know where he wants the pass."  Players need to have a target for their passes, and a stick waving around in the air doesn't make a very good target.  Holding the stick with one hand helps you to keep the stick close to or on the ice.  Of course, you must learn where on the ice to keep the hockey stick and when to put the other hand on the stick.  Having the stick on the ice at all times also increases the chance that a loose might end up on your stick rather than on someone else's.

Regardless of whether you skate with the stick in one hand or two, when you skate straight forward or straight backward the arm swing is also forward and backward.  Referees, who do not use a hockey stick, should learn to use the same forward/backward arm swing.

A forward/backward arm swing enhances forward momentum.  A side to side arm swing enhances sideways momentum.  So, when moving sideways (in hockey we call this lateral mobility), you should move your arms sideways (along the desired direction of travel).

Tips for achieving a forward/backward arm swing:

Most players understand that it's important to fully extend the legs during each stride.  Because the arms and legs naturally work in unison, it's also important to fully extend the arms through each arm swing.

Finish each forward and backward swing of the arms with the elbows straight and with the palms of your hands facing upward.

Move the arms forward and backward in such a way that the elbows stay close to your ribs as they move.  If the elbows stay wide as they swing your arms will be forced to move sideways rather than forward and back.

Move your arms in rhythm with and in the same line as your legs.  Since the legs move diagonally (back and out, forward and in) the arm swing, when performed correctly, will translate into a diagonally forward and backward motion.

Arm Swing (Video Clip)

The arms should never cross the midline of your body because if they do, they will move sideways, creating sideways rather than forward momentum.