What I have is actually a modified pre-amp thanks to the help of Guido from Modifying PYLE PP444 Preamp - Reparación de RelojesThe Korg and other cheap mics are what's called "unbalanced" (two wire) while professional recording technicians use balanced (three wire) cables and connectors. Balanced setups are much lower in noise. The mics that come with time graphing machines are also balanced, but more expensive and more difficult to connect to your computer. In short, the answer is no you can't rewire a cheap unbalanced mix to balanced, but simple tone controls like on my little Behringer mixer/mic preamp can reduce the noise enough to make the program work. Probably the best solution is to simply spend a little more and buy a balanced mic intended for the purpose for $69. You will still need to buy a preamp to interface this balanced mic with your computer. Now we're up around $100 for the mic and the preamp/mixer, which is close to the cost of a complete machine, but I prefer the software to the box.
I cut two ceramic capacitors out of the curcuit and replaced one electrolytic capacitor with a 105 ceramic. I also removed the rubber dampener from the clip on mic.
All of these changes increased the overall sound quality and seemed to better isolate the actual sound of the watch.
What I currenty have is definitely usable with all of the available timing software, but simply listening to the audio or trying to add it into a video is an annoyance due to the humming noise.
Perhaps my next project will be to build a proper stand for the watch/mic combo so I can properly time various positions of the watch.
If you're interested, here's are some videos demonstrating all the changes I made to the microphone/pre-amp.
The last half of video 5 is what I'm currently using (after the capacitor replacement) and it sounds decent. Still a lot of unfavorable noise though.