Can a Spell with “Self” Range be Cast by Homunculus Servant?

I’m playing an artificer for the first time and trying to decide whether or not to use an infusion for the homunculus servant. But I’m wondering about the channel magic ability. It says “The homunculus delivers a spell you cast that has a range of touch.” I’d like to know if I can use a spell with a range of self in place of a spell with a range of touch.

As far as I understand it, broader ranges are inclusive of smaller ranges, so if you can cast a spell at sixty feet, you can also cast it at fifteen feet because fifteen feet is closer than sixty feet. And if you can cast it at a distance of touch you can cast it on yourself, because you are closer than the furthest thing you can touch. So I’m really wondering if the same reasoning that applies to the effect of the spell applies to the ability to cast the spell. If you can cast a spell at a range of touch does that imply that you can also cast a spell with a range of self?