So basically, your proposal is "make zelda more like metroid"
I do agree that putting most of the items in the overworld is a good idea, but putting players on more fetch-quests isn't.
I'm not sure I like the idea of smaller dungeons. It makes the exploration aspect of the dungeons much less. Dungeons are supposed to be mazes that you need to explore, with various different passages twisting and interconnecting, with you being able to see an area you can't reach right at the beginning but not actually getting there at the end. Making the dungeons short would defeat the purpose.
It would be easy enough to put tests very early on in the dungeon that make sure you have the necessary items, or to let you enter and leave the dungeon at pre-defined points rather than only at the main entrance and exit. Personally I think the latter approach is the better one. Don't have more smaller dungeons, have fewer larger ones. Dungeons would contain multiple items, and you would have to leave the dungeon part-way through, only to come back to it much later.
A possible solution would be to have even smaller mini-dungeons, which contain a single item, 5 rooms or less, a few enemies (including some specialized for the item), some puzzles to learn how to use the item, then a mini-boss that requires just that item to beat. These would serve purely to give you items and teach you to use them. Many of these would be available up-front, but others would need items to access.
You would get some items from characters, but those would restricted to mini-games, side-quests. There would only be a few of these. There be lots of side-quests, but these would be restricted to getting upgrades for your existing items. So many if not all of your items would initially come at a basic level, but you could increase their power or give them new abilities by doing side-quests. This would also allow for alternate ways to accomplish certain tasks. For example, say you need to freeze something. You could do the mini-dungeon for the ice staff weapon, or you could do side-quest and get the ice arrow upgrade. To cross a large gap over a volcano, you could either do the mini-dungeon to get the Roc's cape, or you could do a side-quest to get you a longer version of the hook-shot.
The main dungeons would be larger than the existing ones, would contain multiple items, and like the mini dungeons would have mini-bosses dedicated to those items. However, like in the game boy zelda games, after defeating a mini boss you would open a permanent two-way portal between the former mini-bosses and the exit of the dungeon, allowing you to then leave and come back later. This would also allow you to jump between different areas of the dungeon.
You could not beat a dungeon in a single go, you would need to leave and visit other dungeons (mini and full) to get items necessary to proceed. The final boss would need multiple items to defeat, including ones from other dungeons and mini-dungeons, and likely you would be able to beat the bosses in several different ways. A portal would automatically open when you reach the room immediately before the final dungeon boss, letting you leave to get items if you don't have everything necessary to beat the boss (it would also let you save and refill your health, so you could easily try again if you can't beat it).