I'm not a complete expert at OoT (mostly because I haven't done just about any of the tricks I'm about to mention), but I know plenty of tricks so I know what can be done, just not how hard everything is. This run will be as hard as you want to make it as you can pretty much beat the dungeons in any order you want, and can cut a number of dungeons short by skipping their boss keys by touching the boss room loading trigger (A trigger that's always active regardless of what room you're in).
The Kokiri Sword can be skipped. Traditionally it has been obtained solely for the purpose of the Door of Time skip, but a swordless method was discovered this year. Getting past Mido without the sword or shield can be done with bomb hovering and probably some aqua hess. However in this instance you'd probably end up trading the Kokiri sword for Deku sticks, and you probably don't want to have to deal with Deku Sticks.
The biggest arsenal you have in this game are hovers, so the first thing you should work on is getting bombchus from the well. Aquaescape is a really cool way to get to Kakariko fast, and it's super easy to do. From there you just go straight to Kakariko, do a Cucco dive or something to enter the well.
The objective of the well is to unload the main room via walking while talking so to be able to enter a crawl hole that would normally be flooded, enter and leave the "Boss" room to re-load the water, and then perform a vine clip to fall OoB into the water, then swim your way to the bombchu chest without getting trapped in an unloaded room.
From there you can backtrack to Zora's Domain. There are a number of ways to bypass the waterfall. You can either do I think a megaflip?, or you can do an OoB trick to avoid loading the waterfall segment of Zora's River.
The Gold Scale isn't necessary at all. The Ruto bottle can be skipped with some neat looking tricks, and I'm almost certain that cutscene dives replace any need for the iron boots or gold scale.
Jabu Jabu's Belly can be beaten with just the sword, shield, and boomerang. The boomerang is mandatory for defeating Barinade.
One thing you may consider doing is completing the Great Deku Tree and Dodongo's Cavern as an Adult. Technically you can also beat Jabu as an Adult, but getting inside his belly requires the most absurd trick ever. Wish it was as easy to do as the 3ds version.
The Great Deku Tree as an Adult may or may not require fire based weaponry, I can't remember. If there's a way to get by the first basement web, I think it might be a vine clip trick off the long vine spanning the basement/first floor. The Hylian Shield and the Deku Shield aren't required I don't think, but if you're restricting your dungeon access to the order given, then I'm almost certain you need either one to get past the 231 room, as the Mirror Shield will break the scrub's deku nuts.
I can't think of any potential bottlenecks for Adult Dodongo's Cavern other than the eye switch rooms with the ring of fire(s). I'm pretty sure you can use either some jump slash tricks to get by.
For Adult Dungeons, Water first is actually not as tough as you would think, due to the fact that you can do a Boss Key skip to shorten the level down to 2 rooms. If you don't decide to do boss key skips, it's probably living hell to beat it without Iron Boots. Furthermore, there is at least one eye switch, so you'll have to work your way around it.
Fire before Forest is Zelda Universe easy as absolutely nothing in the dungeon requires arrows. The Fire Temple's boss key skip can be done somewhere in the room that you obtain the Megaton Hammer. The Megaton Hammer is required to defeat Volvagia.
Forest is another two room dungeon thanks to the Boss Key skip. The hookshot/longshot can replace the bow and arrow beating Phantom Ganon, but I'm not sure how spirit works without the bow. I believe Ganondorf requires using RBA if you skip the bow.
Spirit and shadow temples don't exactly depend on one another in any interesting way. Spirit doesn't require hoverboots, and invisible monsters can be Z-Targeted without the Lens. Instead, their difficulty will depend on what items you obtain during the run. Reaching the Spirit Temple without the Longshot or Lens of Truth is a little tricky. The Longshot is normally used to cross the first sand trap, so you have do a trick where you backwalk across the edge of the quicksand and sidehop just as you get across so you don't go out of bounds. Desert without lens requires good eyesight and memory.
The Spirit Temple is a really interesting dungeon as there are two ways to enter it, and you can completely skip the silver gauntlets if you want. This temple has a boss key skip as well, but it's incredibly risky do last I heard.
The Shadow Temple can be entered without din's fire. You can either hover up to the ledge around the graveyard, or pull of a special superslide hover deal that allows you to sort of teleport in mid air to where you can just jump to the ledge.
I'm probably missing a lot of important stuff.
