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Yes, exactly. Cut both wires off the choke button but leave the button in place. If you look at the key switch, if a terminal type with screws there will be a terminal with a C this is the choke. After securing all the leads to the terminals, wrap the key switch in a couple rounds of electrical tape to protect from touching anything in the box. Use ring terminals on the switch.
There is a "Mercury" type switch with leads already in position, however these are sometimes hard to fit in the box. I use the terminal type.