Should I remove the resonator from my cars exhaust?

Some replacement pipes actually delete the resonator from the system, so other than a small change in sound it will have no affect on the system. As far as welding up holes in the pipes, if they are rusted out to the point of having holes forming in them the metal will be extremely thin in those areas and welding the holes shut will be all but impossible. If your going for a DIY kind of fix you may need to cut out small sections of the pipe and replace them. Get a rough idea of the cost of the DIY in your head then call around to muffler shops and decide if the savings if any is worth the time of doing it yourself.