I've not seen wire on an original Haines. But the Haines architecture is not particularly different from other Lancaster makers of the same period. It's the execution, the carving and the engraving that distinguishes Haines from many others, in my opinion.
If I was considering such a thing I'd have to decide whether to try to imagine how Haines might have incorporated wire into his designs or go free style as Bivins did, using the Haines basic lines and some of the motifs and getting creative (in his case, way beyond what has been documented). Bivins used plenty of wire inlay and you might want to study examples of his work for ideas.(aside-If Bivins had chosen Armstrong or Sell rifles as the basis for his are of self-expression, we'd all be looking at Armstrong or Sell precarves everywhere)