You don't have to cut the cable.
You can do one of three things.
A: Build an external box, with a female plug for your keyboard cable. You plug your keyboard into that box, and then a USB cable into the other end and that goes to the computer.
B: You internally mount the teensy, so take the keyboard apart, remove the cable (no need to cut, shouldn't be soldered on), solder 4 wires to the points on the processor to the teensy, and mount things so that you can have a USB cable plugged in to the teensy.
C: Do as you say and splice the teensy into your existing cable. This is not the recommended method, as it can be a bit janky.
Once you do one of those three things, you make sure that soarer's firmware gets uploaded onto the teensy. That's pretty much as simple as downloading the firmware, plugging in to the teensy via USB, and upload it with a software tool made for the teensy.
This really isn't complicated. This is pretty much on board with stuff you'd do in the "My First Electronics" Kits you see marketed for kids at Radio Shack and such.
Soarer has nice instructions, links for the firmware, etc in a post here.If you do need help, people here are willing to offer aid.