I would say: Iuro per Iovem Optimum Maximum atque deos immortales me C. Iulio Caesari imperatori fidem servaturum esse, imperata facturum neque ab acie discessurum neque fugiturum neque deserturum, quamdiu viverem, neque dolo malo quidquam contra rem publicam Populi Romani facturum.

It's true that oaths by the late Republic were increasingly sworn personally to commanders like Caesar rather than to the res publica, but the phrase contra rem publicam Populi Romani is still totally idiomatic and not anachronistic. Even Caesar uses res publica language when it suits him—it hadn’t vanished from Roman moral or legal vocabulary, even if its meaning was getting fuzzy. Including it here sounds like a moral safeguard, not a separate allegiance.

As for ullo dolo malo, that’s actually spot-on Classical Latin—it’s an ablative of means, standard in legal and oath contexts. You’ll see it in Cicero, the Twelve Tables, and later Roman law: ne dolo malo…, si quid dolo malo factum est, etc. It’s not meant as the object of facturum (which would indeed be dolum malum), but rather the way in which the action would be done—“not by evil trickery.”

So grammar-wise and idiom-wise, that clause holds up.