What is the shunt trip's coil voltage? If 120V, then you could run most all of the way to a relay coil with low voltage, then control the 120V locally.
Obviously you are subbing the wiring from somebody who is designing the controls. They will have a schedule of what cable they want you to use for which purpose, e.g. It will be connect-air or anixter, then a jacket color, then the size and number of conductors.
Sure, you could just do your own thing, and you might get called on it.
Check your specs and the job binder, should be in there somewhere.
If you are not sure, you could always run #16 THHN and call it good!