I have a crack in my exhaust manifold and have.

You are a OBD 1, the crack in the exhaust manifold will definetly effect the operation of the 02 sensor, and the vehicle will run rich, now as for the small amount of white smoke you can be describing condensation. Now do you have this white smoke at all time and are you loosing coolant? As for the muffler will it help with the emission test? No, The muffler is just for noise, if you dont have a catalytic thats a differnet story, You automatically fail the test.

No you need to fix the crack in manifold and put another catalytic converter on to pass emissions. Also cheange the oil an doil filter then driv for about 15 miles on eway to get engine good andwarm prior to testing. The small amount of white smoke may be due to condensation in exaust during start up. If it does itall the time it may be a small coolant leak. Going into cylinder.