1/2" (.5000) is 12.7 mm. 9/16" (.5625") is 14.2875 mm

I've never had any issues substituting a 13 mm wrench for a 1/2" wrench or a 15 mm wrench for a 9/16" wrench. However if the flats are worn on the pedals or the wrench made to poor tolerances, then you might need to use the correct size if too much muscle is needed to loosen the pedals.

However my Shimano pedals are 15 mm across the flats and don't take a 9/16" wrench. You should check your pedals to be sure. And do you really have anything with 1/2" pedals still?

Don't confuse the thread diameter and pitch for wrench size.