Well, I think I have the answer. I just need to see if I can find this product locally. This looks like the whole answer.
Aphid Chaser uses pheromones to “upsets the insect’s chemical ecology and breaks down communications in aphid colonies. These nontoxic dispensers do not affect beneficial insects <snip>. They act to ward off most common aphid types
I picked up a package of aphid and white fly traps. I will hang one of the Aphid Chasers on the wall and one of the aphid and white fly traps away from the wall and eliminate the problem without spraying. I see this as being an elegant and ideal solution.