As a Combat Medical Technician could one opt out of holding a weapon like Desmond Doss did back in WW2 in modern day?

There are people in the military who do not handle weapons (such as military chaplains), however I am not aware of this being an option for CMTs - but I could be wrong, perhaps if it is something you feel strongly about, try contacting the recruiting team who may be able to find out for you.

Perhaps it is worth knowing a few details as well though.
CMTs are non-combatants, this means they only ever use a weapon in self-defence, or in the defence of a patient in their care.
To care for a casualty safely, you need to be able to handle weapons in order to make that weapon 'safe', therefore, some weapon handling skills are important to learn.