The wiring to the starter is the problem for the starting issue, that doesn't mean the cats are good though. You can do what SAATR recommended, he's absolutely correct, but the easier route is one of the following.
A: with an infrared thermometer check the inlet and outlet temperature of the catalytic converter. Outlet temperature should be higher than the inlet by 20* or more (higher is better in this case with how old the truck is).
B: less scientific, but more fun. Unscrew the O2 sensor(s) and see if your idle improves. Maybe take it for a test drive and see if your throttle response improves as well. You can also get a good indication of how your cats look by seeing if your O2 sensor is fouled up. Make sure you unplug the O2 sensor as well or you'll end up in closed loop with sensor telling the engine you're running way lean and up running rich with the ECM trying to compensate.
C: run a scanner and look at your upstream and downstream O2 sensor readings. IIRC under 80% pops a code, but anywhere south of 90% will give you noticeable symptoms.
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