The participle with ἄν represents the indicative with ἄν ( cross1784 ff.) or the potential optative with ἄν ( cross1824). The present participle with ἄν thus represents either the imperfect indicative with ἄν or the present optative with ἄν; the aorist participle with ἄν represents either the aorist indicative with ἄν or the aorist optative with ἄν. Cp. cross1845 ff.
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].