Is "braided monoidal" a conservative extension of "lax braided monoidal"?

Hi everyone, Is there a known result (or counterexample) saying that the equational theory of a braided monoidal category is a conservative extension of a lax braided monoidal category? As a reminder, a lax braid is a natural b : A * B -> B * A satisfying coherence conditions with the units and associators, and a braid is a lax braid where b is an isomorphism. The motivation for asking this question is that string diagrams are a proof technique for braids, and I'd like to be able to use them for lax braids too, but this requires braiding to be a conservative extension of lax braiding. Cheers, Alan Jeffrey. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]