After struggling with this for a long time, my trial translation is: “if [with, or by means of] what you say, you persuade us.”
I’m trying to justify this by LSJ, ὅς IV.2
[select] the neut. of the Relat. is used in Att. to introduce a clause qualifying the whole of the principal clause which follows. . . .—so also the neut. pl. ἅ may mean with reference to that which
Bailly: 7 avec double accus. πείθειν τινά τι, persuader qqe ch. à qqn, persuader ou convaincre qqn de qqe ch. HDT. 1, 163 ; ESCHL. Pr. 1063, etc. ; XÉN. Hier. 1, 16 ;
Liddell: with neut. pron., persuade one to or of a thing, τοῦτό γε οὐκ ἔπειθε τοὺς Φωκαιέας Hdt.1.163, cf. A.Pr.1064 (anap.), Pl.R.399b, etc.