In myelinated nerves, saltatory conduction occurs (the impulse jumps between adjacent Nodes of Ranvier) which does not occur in smaller non-myelinated nerves. Not sure if the diameter of nerve has anything to do with the conduction velocity. But in case of electric wire, larger the diameter, the lesser the amount of resistance to conduction.
if I understand your question well, I think there are many diseases that preferentially affect the small unmyelinated fibers like early manifestations of DM, some drugs and toxins and some connective tissue diseases