Sure, it's possible that some hum could be induced there. However, the hum is coming from somewhere, in order for it to be induced on that cable. The wires themselves are not causing the hum, they are just picking it up. Unless there is a wiring problem or dirty connectors.
One thing about your description, is that you seem to state that the loop is somehow separate from the rest of the internal tonearm wiring. This is very unusual. I have never seen a tonearm wired so that the loop is not a continuous section of wire that includes the tonearm wiring. How do you know that the hum is not coming from the internal tonearm wiring? Is there some kind of plug that the loop plugs into at the tonearm, and you can isolate it from the internal tonearm wiring? If so, that may be part of your problem. There should be no breaks in the tonearm wiring from the cartridge clips, all the way to the final RCA plugs. Any breaks cause signal loss, and if they get dirty or have some oxidation can cause this hum.
Something sounds very unusual about this circumstance. What is it? If you have made modifications, tell us so we can properly determine the problem.
Other than that, I would look at trying to eliminate the source of the hum. As Ron said, it is likely a stray hum field from some of your equipment or power cords. If all else fails, get a different tonearm.
One thing about your description, is that you seem to state that the loop is somehow separate from the rest of the internal tonearm wiring. This is very unusual. I have never seen a tonearm wired so that the loop is not a continuous section of wire that includes the tonearm wiring. How do you know that the hum is not coming from the internal tonearm wiring? Is there some kind of plug that the loop plugs into at the tonearm, and you can isolate it from the internal tonearm wiring? If so, that may be part of your problem. There should be no breaks in the tonearm wiring from the cartridge clips, all the way to the final RCA plugs. Any breaks cause signal loss, and if they get dirty or have some oxidation can cause this hum.
Something sounds very unusual about this circumstance. What is it? If you have made modifications, tell us so we can properly determine the problem.
Other than that, I would look at trying to eliminate the source of the hum. As Ron said, it is likely a stray hum field from some of your equipment or power cords. If all else fails, get a different tonearm.