Rubuta ci gaba don wannan sakin layi - 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 yi musayar Cunneyworth, Gary Suter da Whalers zagaye na uku a cikin 1995 NHL Entry Draft
zuwa Chicago Blackhawks ga Frantisek Kucera da kuma Jocelyn Lemieux.