There have been two Rep Gov in Hawaii. William Quinn and Linda Lingle. You are probably too young to remember Quinn who was Gov from 1959 to 1962.
The first governor, Quinn, was appointed by a Republican US President, not elected.
Although he won the state's first gubernatorial election in 1959, the fact that he was the incumbent, appointed Governor of the territory in 1957, makes his election almost a "gimme".
Technically, he was elected governor. Realistically, he was already in the job when the first election was held.
However, it didn't take long (one term) for the Democrats to lay hold of the office for 40 years.