Female descendents of the Bounty mutineers were allowed to vote for their ruling councils on Pitcairn Island from 1838 and Norfolk Island from 1856 (when they settled there). The Isle of Man, an internally self-governing dependent territory of the British Crown, enfranchised women property owners in 1881.
Women in the Cook Islands, then a British protectorate, were allowed to participate in elections for island councils and a federal parliament from 1893. This law was enacted several days after New Zealand's Electoral Act was passed, but Cook Islands women got to the polls first, on 14 October.
In addition, a handful of United States territories and states had enfranchised women by 1893: the Territory of Wyoming in 1869 (confirmed on admission to statehood in 1890), the Territory of Utah in 1870 (annulled by the US Congress in 1887, reinstated on admission to statehood in 1896), the Territory of Washington in 1883 (declared unconstitutional by local Supreme Court in 1887), the Territory of Montana in 1887, and the State of Colorado in 1893.
Australia was quick to follow New Zealand: South Australia enfranchised women in 1894, Western Australia in 1899, and the Australian Commonwealth government in 1902 (except Aboriginal women).