HOWEVER, I would offer that from the TSR AD&D adventures I have run, AD&D is a) much more "hack and slash"/murder hobo like, and b) much more deadly/much more "random", as compared to a WotC 5e campaign. Not to say that is bad, but I find that if you want to do it, you will want to tell your players this so they have the right expectations going into an AD&D style campaign.
I personally (as a DM) prefer having (some amount of) plot line in my adventures, so I find myself filling in a lot of gaps myself if there needs to be a plot line (which I personally enjoy). I also prefer not to kill my players characters (granted, I also level set that doing things you expect to get you killed will in fact get you killed), so I tend to tune back a lot more of the "deadly" traps (i.e. in some of the really deadly dungeons, just a bad roll of dice on a failed trap will kill you. I am not a fan of that, so I tune it back that it will eventually kill you, but you have a chance of reacting and your teammates can save you).
But I will also offer, I have had players who want to run it "old school", so I don't do any of that and run it as a 1:1 translation, and we have had a lot of fun with it too!
The all-time classic of this genre was the Tomb of Horrors. As a player, you basically have to be ultra paranoid about every single action you take. And even playing in that mode, you're likely to lose a significant portion of the party. And yes, you definitely want all of the players to buy in to that style of play up front before trying to run an adventure like that.
I would agree you should be able to run the module as-is and insert a monster of the same type from the 5e monster manual, but certainly not use the 1e stats straight up.
1e monsters wouldn't stand a chance against a 5e party otherwise.
"I got a 19"
"OK, well, it's on you. Roll a d6"
"I got a 5"
"Well, you're going to die quickly then."
"What did I need to live?"
"To look up."
I think that is the bigyest thing DMing. I don't mind playing some of the very deadly dungeons, but you do really have to work with the players to set expectations on it. Same with how you DM, play style, etc.