The Orthodox New Testament, an extremely literal translation done by some schismatic Greek Orthodox, suggests "mighty through God", as in:
For the weapons of our warfare [are] not of the flesh, but mighty through God to [the] pulling down of strongholds.
In the Nicene Father series, the verse as it appears in John Chrysostom's Greek commentary is translated "mighty before God", which conveys more or less the same meaning, I think. The full translation:
“For our weapons are not of the flesh.”
For what sort of weapons are of the flesh? Wealth, glory, power,
fluency, cleverness, circumventions, flatteries, hypocrisies,
whatsoever else is similar to these. But ours are not of this sort:
but of what kind are they?
“Mighty before God.”
And he said not, ‘we are not carnal,’ but, “our weapons.” For as I
said, for the present he discourseth of the Preaching, and refers the
whole power to God. And he says not, ‘spiritual,’ although this was
the fitting opposite to “carnal,” but “mighty,” in this implying the
other also, and showing that their weapons are weak and powerless.
And mark the absence of pride in him; for he said not, ‘we are
mighty,’ but, “our weapons are mighty before God.” ‘We did not make
them such, but God Himself.’ For because they were scourged, were
persecuted, and suffered wrongs incurable without number, which
things were proofs of weakness: to show the strength of God he says,
“but they are mighty before God.” For this especially shows His
strength, that by these things He gains the victory. So that even
though we are encompassed with them, yet it is He that warreth and
worketh by them.