Would I need to remove the 3 or 4 pin connector, and splice a single pin header to work on the OptiWiz?
You can pull the pins from the 1x3 and 1x4 pin Dupont headers and put the X1, X1, Y1, and Y2 pins in the 1x4 header.
If you have any 1x1 and/or 1x2 Dupont headers, use those for the ground and two 5v pins.
If you don't have a 1x2 header or enough 1x1 headers, you can re-use the 1x3 header for the 5v lines and leave the unused connector position hanging.
Ultimarc UTrak encoder pinout:

Optiwiz3 pinout:

Scott
EDIT: Looking closer at the cable from ArcadeRenovations, other than red wires for the 5v lines it uses non-standard wire colors. You'll want to move the pins in a specific order so you don't get them crossed up.
1. Pull the 4-pin connector ground pin and put it in a 1x1 header.
2. Move Y2 to the position that 4-pin connector ground was in.
3. Move Y1 to the position that Y2 was in.
4. Move X2 to the position that Y1 was in.
5. Move the 4-pin connector 5v line to the center position of the 1x3
or to a 1x2 header if you're using one.
5a. If you're using a 1x2 header for the 5v lines, move the 3-pin 5v line to the 1x2 header.
6. Move X1 to the position that the 4-pin connector 5v line was in.