I believe that in order to be recognised as circumnavigation, the requirement is to reach the same latitude in both hemispheres. Even a quick "dip" will do
Basically the rules require a minimum distance of 36,770 km, all control points to be at latitudes less than 66 degrees 33 minutes and to cross all meridians, no need to cross the equator.
https://www.fai.org/sites/default/fi...ion_2_2013.pdf