Nyorai kuenderera mberi kweiyi ndima - Muna 1993<unk>94, achitamba nguva yakazara pasi pemurairidzi mutsva Pierre Maguire, Cunneyworth akaonekwa mumitambo makumi matanhatu nematatu neHartford, achihwina zvibodzwa zvipfumbamwe nemapoinzi gumi nemanomwe. Musi waKurume 11, 1994, neWhalers iri kunze kwekutsvaga kwekutsvaga, Whalers GM Paul Holmgren akatengesa Cunneyworth, Gary Suter uye Whalers yechitatu yekutora mu 1995 NHL Entry Draft
kuChicago Blackhawks nokuda kwaFrantišek Kucera naJocelyn Lemieux.