What is the percent risk of my child catching polio versus the percent risk of my child having a bad reaction to the vaccine?

Enough to ponder. An asymptomatic polio carrier can get on a plane in the third world, fly to your state & enter your mall/store/ population & the germ can be in your local for wks & be passed to your kid. The inactivated polio vaccine has negligable issues & prevents a deadly disease. If we are lucky and can eliminate polio from the world we can stop the shots. Until then accept that the germ can be next door.
Wait a Minute. In your comment you refer to the combination vaccine pediarix, but you question only the polio component. If you refer to the 1% statistic and include diptheria, polio, tetanus, pertussis, and hepatitis b diseases in an unimmunized population, your odds are much greater than 1%. So it is safer to immunize.
Tiny...however... My take on this is that the risk of an adverse reaction to being immunized against polio is very tiny; the risk of actually contracting the disease is also ver tiny...But you don't want to go through the latter. My advice is to discuss the matter with your pediatrician; then make your decision.
Both are very low. But your child is not living in a bubble and wildtype polio still exists. The vaccine is quite safe.