I would completely discount the movie's take on Sauron's melee abilities.
To touch on what
Mith said,
The Silmarillion states that during the siege of Barad-dűr,
Quote:
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Sauron himself came forth; and he wrestled with Gil-galad and Elendil.
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Silm Of the Rings of Power and the Third Age
In the Council of Elrond, when telling of those events, Elrond says only that
Quote:
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I beheld the last combat on the slopes of Orodruin, where Gil-galad died, and Elendil fell, and Narsil broke beneath him.
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FOTR The Council of Elrond
That would seem to suggest that there was some sort of action involving weapons on Sauron's part, but apparently it wasn't noteworthy enough to specifically mention afterwards.
Sauron mainly relied on minions and servants to do his dirty work, and maybe on those rare occasions where he himself fought, like the battle with Gil-galad and Elendil, his weaponry just wasn't singular enough to warrant any special attention by witnesses.
Alternately, maybe he himself didn't make use of weapons, thinking he could accomplish his victories with his aura of terror, or that failing, with brute strength.