You don’t get to take the “no effect” over the “small effect” just because you’re an atheist. That is precisely what taking faith over data looks like!
I take what I consider to be the simplest explanation in the absence of a credible alternative, that prayer does nothing when the recipient is unaware of it.
I take that view because I've never heard an alternative explaination that didn't appear to break the second law of thermodynamics.
A magical, invisible, omnipresent, omnipotent "all known laws of nature defying"-being that answers prayers, requires significantly more evidence than a small effect in some meta study.
A more properly scientific line of reasoning would be to instead say that you'll assume the small-to-nonexistent effect is nonexistent until somebody produces a model capable of predicting the proposed small effect, or a myriad other arguments along the same general lines.