Let me play the ignorant, Rob
Searching (PDF) the work "Romeo and Juliet" by W. Shakespeare (1591) the term seax doesn't appear; only dagger, knife, sword ...
Surprisingly the (circa 5000 pages) "Oxford Universal Dictionary" (1933-1969) doesn't contain this term.
One can see in Wikepedia that the term seax is Old English, a language form that spans between V-XII centuries.
Most probably you will soon find evidence that the term was dropped during the period you well suspect
.