Could a Paladin use the Divine Smite ability on a disarm attack?

The Oath of Redemption Paladin that I DM for has asked me for clarification on disarming rules. I’ve decided to use the optional rules from page 271 of the DMG, which state:

Disarm
A creature can use a weapon attack to knock a weapon or another item from a target’s grasp. The attacker makes an attack roll contested by the target’s Athletics or Acrobatics check. If the attacker wins the contest the attack causes no damage or other ill effect, but the defender drops the item.

However, I am wondering if he would be able to activate his Divine Smite on that disarm.

Divine Smite
When you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage.

Technically the Paladin has hit the target with a melee weapon attack which leads me to want to rule yes. The disarm rules do state that the attack causes no damage or other ill effects, but the Divine Smite wouldn’t be strictly part of that attack. I feel like I am leaning towards allowing Divine Smite to work after a successful Disarm, but wanted to see if there is any precedent for something like this as I have found no specific rulings to this question anywhere.