I'm actually into the idea of an instant death, be it through no heart containers or through enemies all doing insane amounts of damage. It would certainly render the question of health drops moot. However, designing for this would be a whole other challenge.
I think challenge is a really important aspect to any game, because there is character in challenge and in difficulty curves. There are all these factors. It sounds to me like you're interested in the player building a great deal of skill in order to beat the game. Like this may be the driving force for your game design.
My next question would be how you want the game to progress. Like, will it be terribly difficult at the beginning, mellow out a little as you gather more items, and then ramp up difficulty at the end in an utterly chaotic exercise in pain. Or would you be more interested in dangling the carrot just out of reach, a steady increase in difficulty, every dungeon just a bit more heinous than the last. It's very exciting, to say the least, perhaps more so because I am so new to Zelda Classic. .
However it goes, I wish you the best!