It is possible that elves not be related. Unlike reality, there were a group of elves created first that awoke at Cuiviénen. In our world (whether or not you think Adam was created as the first human, use this for an analogy), it would be like 100 Adam's and 100 Eve's being created in the beginning in the Garden of Eden as opposed to 1 each.
Arwen (and probably Legolas) are only a few generations removed from those that first awoke Cuiviénen, and it is certainly conceivable that they are totally unrelated. Legolas' ancestry is traced no further back than his father, Thranduil, and his grandfather, Oropher.
Since no relation is written or even hinted at, I advise one not to infer any if they wish to stay parallel with the mythological world Tolkien created.
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...take counsel with thyself, and remember who and what thou art.
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