Nothing changes during the Calamity Ganon fight for those who challenge him again. However, completing all Divine Beasts prior does add a bonus scene as the Divine Beasts weaken Calamity Ganon.

What do the Divine Beasts do against Ganon?

If you go with all 4 divine beasts free, the boss’s health is reduced. Also, if you don’t release the divine beasts, you fight the bosses of the beasts you did not free before facing Ganon, and his health is not reduced this time.

Is it possible to defeat Ganon without the Divine Beasts?

You can beat Calamity Ganon with a stick while wearing no clothes and having no Divine Beast powers so not having a shield is perfectly fine.