I hesitate to answer, because the only answer I can think of is tangential to your question.
Really, classic D&D relies on the DM is making certain kinds of decisions, and part of that decision process involves rolling to decide things behind the scenes. I absolutely love semi-diceless mechanics, but there are so many parts of class D&D that I just can't think of any way to put the dice in the players' hands.
For example, assuming random encounter tables are part of classic D&D, how would this be turned into a player roll? I can't think of any character action that could be meaningfully made to serve the same purpose. The alternative to making it character action resolution is to just hand the die to the players and say, "roll, and tell me what is says," which doesn't nearly harness the awesomeness of semi-diceless mechanics.
Similarly with saving throws and morale checks for monsters. I can imagine saving throws becoming a "overcome resistance" roll for the players. However, that would quickly start feeling like "rolling to see if the spell works" and give a very different feel to D&D magic.
With morale checks, I can imagine an "intimidation check", but that would take away much of the surprise and uncertainty when monsters retreat: are they running? retreating? regrouping to return soon? faking a morale break to lure the PCs into an ambush?
So, I'd say that classic D&D is not well designed to hack-in semi-diceless mechanics. It could either be done superficially by just handing the players the dice when the DM would normally roll, but that wouldn't gain much. It could be done more meaningfully, but at some point that wouldn't feel like classic D&D anymore, and at that point you might as well choose a system that does it natively.
As an example of a "D&D-like" game that is based on a semi-diceless system (although it does retain DM rolling on random tables as an option to respond to a player's failed roll), you might take a look at Dungeon World.