Kammala jumla mai zuwa: A cikin 1993 <unk> 94, yana wasa cikakken lokaci a ƙarƙashin sabon kocin Pierre Maguire, Cunneyworth ya bayyana a wasanni 63 tare da Hartford, inda ya zira kwallaye tara da maki 17. A ranar 11 ga Maris, 1994, tare da Whalers da kyau daga farautar wasan kwaikwayo, Whalers GM Paul Holmgren ya siyar da Cunneyworth, Gary Suter da Whalers zagaye na uku a cikin
1995 NHL Shigar da Shafin zuwa Chicago Blackhawks don Frantisek Kucera da Jocelyn Lemieux.