You can change the settings in Mach to ignore the noise. It's in General config, debounce. A setting of 1000 is often good. The pullup resistor is a very good idea. Do this first.
HiymeKabibble, I've worked on computer systems for 30 years and the shield ground on one end only has always been the way it's done. These days, much to my surprise, they advise grounding both ends, and making sure all frame earths are tied together well. It turns out that at the Ghz frequencies that we have noise problems with today, single ended shielding isn't effective, and tying frame grounds together so that you don't get any current through the shield when grounded on both ends gives better results. I have to keep repeating this, or I will forget it myself. It's so weird to change something as fundamental as this, but you know, a Ghz here and a GHz there, and pretty soon you are talking high frequency noise. Ghz signals don't behave all that well with conventional wiring, so we shouldn't expect the noise to behave the same.