Lived in HI for several years and shipped a car to the mainland so basically the reverse of your situation.
As others mentioned, most things are more expensive in HI. (Have you checked out rents? You're going to be paying a lot) I doubt you could buy a comparable car for $9400 so I'd say ship it if you need a car. Another thing to consider is that you know the car you have. If you want something comparable then you may as well stick with what you have and pay the shipping.
But you are questioning whether you need something comparable. You are contemplating buying an older cheaper car, mentioning you can do most of the work yourself. I wonder whether you would sell your Yaris and get an older/cheaper car if you were staying where you are? I don't see that moving to HI has any bearing on this decision. You either value the reliability and gas mileage of a late model car, and are willing to pay the price, or you value the savings that goes with an older car, and are willing to deal with the repair issues that will be part of owning an older car. You should make that decision w/o respect to where you'll be living.
However, going w/o a car, or not, is a decision that needs to take into account your move to HI. TheBus as it is called (or was called, when I lived on Oahu) is a very good system. You won't be able to take your kayak on the bus but you should be able to get around pretty well w/o a car. It's not as if you'll be biking to class in a snow storm. Will your study schedule really allow for frequent kayaking?
Parking is a headache. Make sure your apartment building includes a parking space for you - and you may have to pay extra for that.
If you decide to have a car, be aware that when entering a freeway in HI you'll have a tendency to think you should be doing 70 in order to merge. You'll quickly find the traffic is so bad that there are cars backed up on the entrance ramp. Be careful.
I had a car because I was in the service and had to report for duty at various times, day or night, so I couldn't rely on public transport. The price of shipping to Seattle was $600 (1985) which greatly exceeded the value of the car ('67 Rambler) but I knew I couldn't get anything better for $600. I used the car for a few more years after shipping so I think it was worth it.