will it be bad for the engine if i ran the car with a small honda muffler on it?

I am planing to use a cut-out valve on the car, Its a cast iron Y shape that connects to the headers, and a cable that goes into the cockpit, its mainly for using straight pipe in the streets, So you pull the lever and the flap switches causing the flow to go into the other "SIDE", and after you race, you can push the lever back, and you end up with your stock muffler again.

But i jsut want a quiet car while im not racing. So what do you think will work best? I just want something cheap.

1974 junkyard 260Z
100% Junk Will be restored to a new car by next year.