turns signal switch?

I went to remove a turn signal switch from the 64 Valiant. The shop manual is pretty useless on this one.

The wires feed all the way down the inside of the column, out a hole then have a large plastic connector on it. The only way I can figure to get it out, is to push out all the wires from the connector, then pull the wires up and out. No way can that connector fit through.

Anyone have a shortcut?
thanks
No, The way you have it figured is correct. You need to trigger the wire terminals to get them to release from the plastic connector.Compare the wire colors between the old and new switches first. Then draw a diagram on a piece of paper so you get the color codes back where they come from when you get the new switch in place. As redrag64 mentioned, connect a strong string or wire to the old switch wires so when you pull the old switch, the string will follow the wires through the column. Retie the string on the new switch and pull the wires back through. I like to bend one wire over and tie my pilot wire to that bent wire. Then wrap the wire ends and pilot wire with electrical tape. Try to keep it from getting too big in diameter or you'll never get it to slip through the hole in the column.