socket-board and wires

Hopped out and looked at the site you referenced. Those socket-boards are great for a project like this. #22 wire is about the limit, and stranded #22 probably won't insert without some of the strands curling up. This is not a problem as long as a) most of the strands are down in the socket; and b) the strands which curl up are trimmed so they don't make contact with other components. Normal component leads on the parts shown are #24 solid. This would be fine for the connections to the switch. I don't know what country you are in, but Radio Shack sells a small spool for $3.00.

I still like the idea of using stranded wire for the connections to the handles, but buying a 100 foot roll to use only 4 or 5 feet seems dumb. Maybe a hardware store (Home Depot, Lowes, etc.) will have shorter rolls and save you a few bucks. The same #24 solid I mentioned above will work just fine, as long as you are careful about repeated flexing near the connection points.

ak