Since you have already ruled that this is an impossibility in your campaign, my answer may be redundant, but I wanted to provide a counter point to the above answer of it being allowed; to show why it might be argued as disallowed. (Also because @Miniman encouraged me to challenge his answer.)
Here is a link to a former question dealing directly with 'Divine Smite' being considered 'extra damage' for the purposes of burst/nova damage as some are calling it.
The relevant description from Divine Smite is as follows:
"...to deal radiant damage to the target, in addition to the weapon's damage. The extra damage is 2d8 + 1d8 per Spell Slot level above 1, to a maximum of 5d8.
Divine Smite, and it's utilization of a spell slot to pull magical energy from to cause, very suddenly, the radiant damage to burst in addition to the weapon damage is what I believe makes it an impossibility to knock someone out with it. That would be saying I could throw on Searing Smite , hit someone with my Warhammer which drops them to 1hp and then when the 1d6 fire damage explodes from my weapon as a result of Searing Smite, I say I wanted to only use 1 of the potential 6 damage it would deal to knock the creature unconscious instead of mortally wounding it.
I don't have that option. Searing Smite would deal it's full 1d6 damage regardless of my intentions. If I wanted to knock a creature out and my first attack only took them 1, I'd have to swing again, or wait until I could, and be cautious not to kill it with anything other than a melee attack.