Tracing the development of the prof's ideas on 'Elvish reincarnation' is a complex matter. HoME X and HoME XII hold most of the relevant writings. As a very preliminary answer, the latest ideas seem to indicate that the body, exactly as it was before, is simply restored or reconstituted:
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HoME XII: "[The] last discussion of Elvish reincarnation refers [...] to the 'restoration' or 'reconstitution' of the former body by the Valar..."
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So the "restored" Half-elven body would be more or less exactly as it was prior to death.