What would be the practical reason for doing so? He would not have been able to see it or use it under his spacesuit, it would have been useless. Also, I think safety reasons would have compelled him to remove it because it could become trapped at some point under the suit area near the glove bayonet mount during the walk (or even just uncomfortable) and the only way to fix such an issue would be to return to the LEM, pressurise it (using up precious air), remove the suit (a lengthy undertaking), just to then remove the nuisance watch. Kill a precisely scheduled and choreographed moon walk for a dumb watch? No, far more likely that he would have removed and left it as a spare in the LEM before suiting up.
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