Does Wrathful smite work with a Beast Master's Share Spell Feature

The only wording on the Beast Master's Share Spell feature is that "When you cast a spell targeting yourself, you can also affect your Primal Companion beast with the spell if the beast is within 30 feet of you." I'm genuinely curious if this can apply Wrathful Smite. Admittingly, it also doesn't make sense to me. But then again,  I don't see a limitation on the Shared Spells feature that would say otherwise. The only limitation I can see is from Wrathful Smite itself which says "Bonus Action, which you take immediately after hitting a creature with a melee weapon attack or Unarmed Strike." and I don't think a Primal Companion's attacks can be considered unarmed strikes or melee weapon attack. 

Idk, what's ya'll's call on this? Seems like a pretty interesting thought experiment at the very least.

Because the target of the spell is Self, does it not mean that you empower your next attack with the spell's effects?

With that idea in mind, wouldn't that mean that if you cast it on yourself, you'll also cast it on your Primal Companion and let them apply Wrathful Smite on their next attack?

I don't see how this is going to work, unless you target yourself.

As explained in previous threads, Range and Targets are different things. Each one has its own separate paragraph in the Spells chapter.

- Range "indicates how far from the spellcaster the spell's effect can originate", but it does not define the targets. 

- The target is explained in the Effect of a spell. Sometimes, a spell with "Range: Self" can target you, but only if the spell says so in its description (e.g. False Life or Shield). Maybe, technically, and if you DM allows it, you could target yourself with Wrathful Smite, but you will take damage:

The target takes an extra 1d6 Necrotic damage from the attack, and it must succeed on a Wisdom saving throw or have the Frightened condition until the spell ends.

And your Primal Companion will also take damage in this case:

Level 15: Share Spells

When you cast a spell targeting yourself, you can also affect your Primal Companion beast with the spell if the beast is within 30 feet of you.

EDIT: for clarity.