I'm not Native Hawaiian but I've lived in Hawai'i long enough to answer your question a bit more comprehensively than the other answers I read from people who pretty obviously are not local Hawai'i people.
Yes,Hawai'i is a state in the USA but I assume you knew that.I don't know exactly what you mean by \"American\" but I'm gonna go out on a limb here and guess that you're definitely not Native Hawaiian and you're probably from the mainland,amirite?
You're only talking about a Hawaiian-style tribal tattoo,not a design from someone's family heritage.Tattoo designs,ku0101kau,are separated into \"kapu\" or forbidden to anyone but a select few and \"noa\",safe for everyone.Some are limited according to one's clan lineage,family membership,age,and social class.You are not going to find those in a regular tattoo parlor anyway.
Most likely the design you choose will not be done in the traditional way but with modern sterile equipment.The design itself may be \"Hawaiian-style\" but not authentically of indigenous Hawaiiann design,especially if you are going to let a non-Hawaiian do the design for you.It should be totally fine and not offensive to anyone.
In Hawai'i there are a lot of people of all ethnicities with tribal Hawaiian tats.No one but a Native Hawaiian has authentic Hawaiian designs.Jason Mamoa's tats?Definitely authentic but then he's Native Hawaiian.Don't copy Jason's tats.Design your own based on the tribal idea.Have the tattoo artist develop a design for you.It will look good and no,it won't offend anyone.And if you ever come to Hawai'i,you will be able to show it off with everyone else.
Aloha ku0101kou!