I'm trying to assign one of my homebrew sub-races the ability to As an action on your turn, you can cause yourself or a creature you touch to regain 1d4 hit points. Starting at 6th level, you add your Wisdom modifier to this effect. I thought that the easiest way to do this was just to give the Healing Word spell but now I'm trying to figure out how when I reach 6th level I can have it assign my Wisdom modifier to the spell. Would there be a way I could lock it doing that until I reach the correct level?

Healing Word is not a “touch” ranged spell by the way. Also, allowing any character the ability to heal even a small amount an infinite number of times is a bit unbalanced (that’s why there are no healing Cantrips).

There is not currently a modifier for increasing healing amount. And level overrides do not support adding the ability score later. So I think unfortunately there is not a way to do what you want right now.