I've always thought of him as wingless; this is (a) because worm to me suggests wingless, and (b) the worms bred in the Iron Hills, and in Thror's map the illustration of Smaug is, as you say, a seprent with wings, but that of "a worm" indicating a "here be dragons" status for the Iron Hills has no wings.
Maybe flimsy evidence, but there's not a lot to go on.
(At any rate, that would indicate a non-winged one survived to breed...if a winged and non-winged mated, it coul very well be that some offspring had wings, some didn't. It would be possible, and helps expalin the 2 dragons survival thing (if it's canon) whilst allowing the various drake strains to live on.)
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