Q 1: Would it be fun?
A : I'm sure most of us at one time or another had wished to do something along these lines. But 'fun' is something only you and he can make happen.
Q 2: (If so,) which one would be best for a one player-one DM game?
A : 'Best' or, easiest (to run)? The S 1-2-3 can certainly be modified to accommodate a single character (and companion). IotA is a grinder, even for adults in a large group. I don't know if it could be easily altered without destroying the wonderfulness of it.
1. Point well taken... 
2. I was hoping for that sweet spot between easy for me to adapt to 1-on-1 while staying as close as possible to the original flavor. You mention S1-2-3. Is there some reason S4 might not be a good candidate here? "Tsojcanth" is one of my all-time favorites. FWIW, the most fun we ever had in college was "White Plume Mountain". Also, FWIW, I've never run or played "Isle of the Ape."
S1 and S2 are easy to do solo with the right level character and the right equipment. Most fights are already with single creatures. S4 would be doable too if the numbers of monsters in some cases were reduced. Drelzna should be interesting.
Very cool.
I'm leaning toward S2 since it's a dungeon crawl, let him get his feet wet with 1E rules, then give S1 a shot simply because EVERYONE should have a chance to die in S1

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