After doing some more research on the slip ring setup others have done, I felt I had enough information and confidence to proceed!
The wires need to be stripped back about 1/4 of an inch so they can be tinned and installed into the DB25 connector.
Its very slow work, the wire is very thin. I wish my wire stripper could do 28 gauge wire. I used the cutter to gently tug the outer layer off. On a few, I pulled away some wire too.
The next step is to find some very small wiring shrink wrap and cut it into small sections. We do not want the wires touching one another or contacting other leads once soldered into position.
As I slid these onto the wires, I clamped them into an alligator clamp so they will not fall out. I ran out of shrink wrap tubing so I will pick some more up tomorrow and begin the process of tinning the exposed wire ends.