Whirlpool Thermostat Cold Control Replacement Tube Barrier

I am in process of replacing a Thermostat Cold Control 2161284 on a Whirlpool Refridgerator. However, I am unable to get the old Thermostat sensor barrier tube 1115241 that was on the old thermostat onto the new thermostat. The new thermostat control came shipped with a tube already over the sensor but it is almost 2 inches shorter than the original so it will not cover the entire sensor to the end. Can I use the tubing that came with the new thermostat or was that only for shipping. Does it need to cover the entire sensor to the end? Or should I head down to the hardware store and get a replacement tube. Any recommendations on what to replace with ? I appreciate your expert opinions. The white tubing in the attached photo is the original from this 19 year old fridge. The clear tube was on the new control when it arrived. Thanks Ken