Shoot Outs - please note

During the shootout procedure, only one puck is to be used. The puck that used to end the game shall be the only puck used unless the puck is in poor condition and a different/new puck is required.

By the time the referee makes it to the other end, the liner that was with the referee can get the puck and take it to center ice.

The other official should be between the benches if benches are on both sides, or appropriate bench if not.  This official should be watching or directing the player who just shot the puck away from the opponents bench. To prevent a retaliation by the shooter should somebody make a comment towards that shooter from the bench or a taunt towards the opposing bench by the shooter after a goal.

Having two pucks causes a distraction from the high linesman from performing his duties as placing a puck at center ice shouldn’t be their priority.  You may also have a complaint from the team required to utilize a "warm" puck.