Because the English "except" causes ambiguity and confusion, as you pointed out, it may be interpreted as "not by works, except if he also has faith". Richard Longenecker addressed this erroneous interpretation of James Dunn, in his Galatians WBC commentary, p.123
The contracted conjunction ἐὰν (the conditional εἰ and the particle αν) with the negative μὴ is properly exceptive in force (cf. 1:19), though it can at times be used in an adversative fashion (cf. 1 Cor 7:17; also Matt
12:4; Luke 4:26–27). As an exceptive, ἐὰν μὴ introduces a qualification either (1) to the whole preceding statement (―a person is not justified by the works of the law except …‖), or (2) to its principal part (―a person is
not justified except …‖). The former is linguistically possible and has been read here by many (so, e.g., J. D. G. Dunn, BJRL 65 [1983] 112–13). It yields the idea that one can be justified by the works of the law (understood not as ―good works‖ but simply as circumcision and the Jewish dietary laws) if these ―badges of Jewish covenantal nomism‖ are accompanied by faith in Jesus the Messiah (cf. ibid.). Such a reading, however, is totally contrary to what Paul says elsewhere about the relation of faith and the law—even contrary to what he says in the latter half of this same verse (as acknowledged by Dunn, who rather lamely suggests that ―in v 16
Paul pushes what began as a qualification on covenantal nomism into an outright antithesis,‖ ibid., 113). So if ἐὰν μὴ is exceptive, the latter reading must be the case: ―a person is not justified except. …‖ Yet since in English ―"except" always is taken to qualify the whole of what precedes, we must here resort to some such paraphrastic translation as ―but only‖ (so Burton, Galatians, 120–21) or read ἐὰν μὴ simply as an adversative (so H. Räisänen, NTS 31 [1985] 547), the former being preferable.
The phrase ean me ἐὰν μὴ only shows adverse exclusive contrast, and it translated unless, if not, but only, and except. None of those mean "except also". There is no reason to consider the Dunn's interpretation, especially when it contradicts the verse, and whole epistle which repeatedly explains that the law cannot justify after the coming of the new covenant of faith in Christ. Using "but" would avoid potential ambiguity.
In addition to the repeatedly unambiguous context that justification out of the law is impossible, we also have the adversative particle δὲ (which Longenecker ignores, and translates as conjunctive "and"). This particle is essentially contrastive or adversative: yet, however, even though, in spite of. The text says, "We are Jews by birth, not dirty sinners, in spite of this, we know that a man is not justified out of the law, but through faith of Jesus". Ἡμεῖς φύσει Ἰουδαῖοι καὶ οὐκ ἐξ ἐθνῶν ἁμαρτωλοί, εἰδότες δὲ ὅτι οὐ δικαιοῦται ἄνθρωπος ἐξ ἔργων νόμου ἐὰν μὴ διὰ πίστεως Ἰησοῦ Χριστοῦ.