When the long wire is unplugged, it will erroniously triggers the ISR.
(Twisting cables also isn't an option.)
Put a cap between 10nF and 1μF between your input and the ground.
An interrupt input will record the slightest pulse on the wire, even if it lasts for a fraction of a microsecond, which makes the problem much more noticable.
Where is the resistor? Is it being unplugged with the wire, or is it right at the board and always in circuit?
what do you tie the shield to?
So both the signal line and the shield are are tied to ground? Surely the same noise is then on both?
What I don't understand is why debouncing code doesn't seem to have any effect
Use an opto-coupler at the UNO, the contacts of the remote switch controlling the LED input of the opto.In other words you will be lowering the impedance of the system, so better immunity form noise.
Is the switch normally open or normally closed? Is it triggered by a high or low?
Because the interrupt interrupts the processor and runs immediately before the debounce code has a chance to do anything.