I've gone around in circles with this and can't seem to resolve this question.
If an alchemist converts an infused poison from ingested to injury, how does that interact with sticky poison? My main question is about RAW as, logically, one might expect it to be expended in an activated magic item based off potions would intuitively be single use with all future sticky poison strikes purely using the base poison, however I can't find a specific rule stating that. Instead, the language used seems to indicate that the spell effect is added to the fundamental properties of the poison, with poison immunity preventing the spell effect from taking place. This of course would be a very powerful combination with sticky poisons and even a basic damaging spell like Inflict Light Wounds, much less more creative spell selections.
Whoever ingests the infused poison is the target of the spell.
As the poison is never ingested when it is applied to a blade then used to harm another creature, the spell infused never has a chance to take effect.
You've wasted the spell and a lot of time/gold to learn a valuable lesson. This is the RAW. As for logically, work with your GM to figure out some mechanics to make it work. Either the additional work you put in to convert the poison ruined the careful work you used to make the Infused Poison (that is a fairly quick process versus the lengthy time you spent beforehand) or it lessened the effect of the spell so that it has highly diminished effect.