In Archie Fisher's beautiful version of this song, we have the verse:
"My dear, I'll wed thee with a ring,
Wi' a ring, my dear, I'll wed wi' ye;
Now thou may wed with whom thou wilt
For I'm sure we'll never mair atwee."*

I'm quite sure the Fisher version is accurate. Of the hundreds of versions of the lyrics of this ancient ballad, he is the only one who makes sense of this verse. "I'm sure we'll never mair atwee" is a variant of "we'll never mair atwin" (i.e. "separate.") It is akin to the line in the ballad of Clerk Saunders, where May Margret says:
                        "Your faith and troth ye never shall get,
                         Nor our true love shall never twin"
He is saying, in effect,I'll marry you (with a ring)--then, afterwards you can "marry" any human you wish; for I'm sure you and I will never be separated." The other versions make no sense. Their verses begin with the Silkie saying "I'll wed you" and end with his saying "You'll never wed me!"