Whirlpool washer lid switch replacement

My Whirlpool washer ([MODEL]LSB6200PQ0[/MODEL]) has a bad lid switch; looks like it shorted out and also slightly melted the 3-wire plug that attaches to the lid switch. Washer works when lid switch is bypassed. Will replace lid switch (AP3180933). Also need to replace 3-wire plug that attaches to lid switch. Is the 3-wire plug available with the wires attached, or do I need to replace the entire wiring harness? Seems like quite an expense to replace entire harness just to take care of one bad plug. Parts list does contain 3-circuit connector "for use with lid switch" (AP3040796) but the picture doesn’t look like the one that attaches to the lid switch and no wires are attached to the plug. Would prefer to get plug with the 3 wires already attached so I can use wire nuts to attach where the old plug was. Thanks for the help.