Can you explain what you mean by single color? Are you referring to wire colors. I don't have any led buttons (might want to have in other CP's but I know nothing about wiring them at the moment).
By single color, I mean LED buttons that use one LED like this red button -- the LED/holder is the first red item on the left.

This type of button uses two wires for the LED -- 5v or 12v power source and a ground.
The LED/holder assembly already has the correct current limiting resistor -- plain LEDs are usually only rated for 3.3v and aren't able to handle 5v or 12v without the proper current limiting resistor.

The single color LED buttons are very easy to wire using .250" quick-disconnect daisy chains available from Paradise Arcade Shop (Bryan's redoing the website at this time so no link for now) -- only LED wiring shown below, no switch wires.

RGB buttons have 3 LEDs (red, green, and blue) and use 4 wires (5v or 12v power, red return, green return, and blue return).
By controlling the current flow/resistance on the individual return lines, LED controllers set the brightness of the red, green, and blue LEDs to create any desired color and intensity.
RGB button wiring example at 3:30-4:00, LED controller in action at 4:50-5:39.
I was thinking of perhaps using a db25 breakout board with screw connectors as I don't have any soldering skills or suited equipment. Any other suggestions would be welcome.
I presume strain relief is not a problem if I use a breakout board.
There are several problems with breakout boards like this.

1. They are somewhat expensive.
2. There will always be one wire that is shorter than the others.
When (not if,
when) you accidently pull on the cable, the force will be applied first to that shortest wire.
The weakest point is where it connects to the screw terminal.
If you're lucky, it pulls straight out and you can find where it pulled out and reconnect it.
If you're not lucky, the wire breaks off and you have to strip off more insulation to repair it -- leaving the shortest wire even shorter.

Proper strain relief uses a clamp (metal piece in middle) on the body of the cable to evenly transfer a tug on the cable or connector to all the wires, minimizing the possibility of damage.
It also prevents the connection points from bending back and forth which will cause metal fatigue and eventually breaks.

Scott