No Surface, No Dispenser, No Fast Travel, Obtain the Master Sword
All in the title. It is possible to visit all islands and defeat Ganondorf without visiting the surface. However, things get more complicated once you take out fast travel. For starters, your access to fairies are drastically cut along with some other items. Take out dispensers and you have to get really creative with what the game gives you in the overworld which gave this run more depth. You get 9 wings from 3 chests on the GSI. This resource is absolutely essential for traversing. There are only a few chests with Zonai capsules in the skies. You gotta use them at pivotal moments or you will most likely strand yourself later on.
Islands are of varying altitudes. Visit the wrong one and you could potentially soft lock yourself. Some islands can be skipped while some are essential to visit for acquiring certain resources and gaining altitude for the next island. The puzzle here is figuring out which ones and which order to visit them. One wrong turn could lead to various other wrong turns which depletes resources which can lead to ending the run. The risk of that happening was what enticed me to keep going. How long could I really go?
There were a few times where I was so sure that I ended the run after making a wrong move and being unable to reload to a previous save only to somehow find something to help me traverse to the next island. I would go from "Fuck! This is it..." to "We are so back!!!" a handful of times which were honestly my most memorable moments playing TOTK.
I recommend this run to the ones really wanting a challenge from this game. You have to use everything you find with the intent of traversing forward. As there were many nuances to learn in the mechanics of traversing between islands with zonai devices, I had to use them in ways I never thought possible which was immensely satisfying. Since I didn't have the paraglider and limited fairies, I had to get good at grabbing vertical surfaces from free fall which was hard at first but got more satisfying and even addicting to do as I got better at it. Name of the game here is resourcefulness and planning ahead in detail. Had a lot of fun with this one :)