How does the paladin’s Divine Smite damage interact with a Zombie’s Undead Fortitude trait?

Imagine this scenario:

A zombie has 8 HP. This is zombie’s turn, it triggers an opportunity attack from Paladin, which uses Divine Smite. Warhammers’ bludgeoning damage is 4, and the radiant damage from Divine Smite is 4.

Does the zombie get to use its Undead Fortitude? Is the damage dealt sequentially, dealing 4 bludgeoning damage then 4 radiant damage, preventing Undead Fortitude?

Does the zombie player (DM?) gets to choose how the damage is applied?