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Household white viniger is 5% acid, about the same as lemon juice which would also work.
You need to kill the mold spores first,than proceed.Just a wipedown.

Those are/were damn great strops,is that mold residue? the white patches.If so I would wipe it down with white viniger (do not saturate)
Than use saddle soap to rehydrate the leather and furthur...