Your Dodge will run fine without the converter, in fact it will have more power and better fuel economy with straight pipe. But you will need to leave the O2 sensor(s) installed in order for it to run correctly. Mine has 2 O2 sensors, one was in the converter, and one was in the pipe after it. I ran true duals with headers and nothing but 2" pipe all the way to the back with no mufflers or converters, and simply welded an O2 sensor **** into each pipe and installed the sensors 1 in each pipe. I run straight pipe (and duals if it's a v6 or v8) on every vehicle I have and always remove the converters, and every one of them has had better throttle response and fuel economy with open exhaust. The myth that removing your converter will cause your engine not to run properly in newer vehicles is simply propagated by the government so that people will not modify their vehicles or remove emission controls IMHO.
Dave