I like SHOK's basic layout, though I don't know if I agree with his reasoning.
First, he used the ranking order from Ankoku's
tournament ranking list (as of 6/28/08), so I'm not arguing with that. However, I would say middle range is basically the C Rank according to that thread, but I'm willing to include the B Rank, too, which extends his above list from Donkey Kong to Pokemon Trainer.
Now let's address the approach and air game... A "*" designates someone who semi-matches the hint criteria.
Donkey Kong - Bair covers both. (though his air game doesn't exactly scream "Wow!")
Fox - Illusion/Shine good for approach, good air game
*Ice Climbers - Squall and Ice make decent approach, but not great. Aerials look better than they are.
Kirby - Excellent approach with dash attack, Hammer, and Fair/Bair. Nair is only real weak air attack.
*Pit - Angel Ring is an OK approach, as is wingdashing. Most aerials are nice, but looke like they should do more.
Peach - Bomber and floating make for great approach, and aerials are still good.
*Ness - Approach is a bit lacking IMO. Air game is decent.
Pikachu - Thunder Jolt is one of the best approach projectiles. Also has an excellent air game.
Luigi - Probably the best all-around aerial attacks in the game, which also make for excellent approach.
Captain Falcon - Aerials are touchier than in Melee, but good when connected. Approach is not as good as it used to be.
Zelda - Her approach is tricky, but decent, and her aerials are monstrous.
Zero Suit Samus - Decent approach game, depending on match-up. Except for Dair, has excellent aerial game.
*Samus - Zair is nice approach, but only for taller characters. Aerials seem much weaker than they should.
*Bowser - Very, very difficult approach, even with Koopa hop. Air game would be better if not for terrible lag (except Fair)
Ike - Quick Draw is good, but predictable as an approach. All aerials are crazy strong, if mostly slow.
Jigglypuff - WOP comes from great air game, and also makes for a fairly good approach.
Pokémon Trainer - Dependent on Pokemon that is out. Squirtle has no problem with aerials or approach. Ivysaur is decent at both. Charizard's approach is pretty bad, but his air game is OK.
Now, from those left over, let's address KO potential:
Ice Climbers - with both climbers: very good, with one: so-so
Pit- decent
Ness - mostly good
Samus - good, but requires some setup for most.
Bowser - what
can't he KO with?
From just these criteria, I'd be willing to put my money down on Bowser, but then we get the last requirement: "unusual strategy". Here are some options and my guesses in order.
5. Pit: I can only guess wingdashing for the strategy, but he only sort of met the initial qualifications anyway.
4. Ness: I might put Ness higher, but I honestly don't know what sort of strategy he would use.
3. Samus: Zair and Missile Cancelling don't take a lot of skill to use, but they take practice to use correctly.
2. Bowser: Koopa Hopping improves his dismal approach, but it's not terribly difficult to learn or to use.
1. Ice Climbers: They really are the best fit for this hint. De-synching is one of the hardest techniques to pull off (that I'm aware of) but it also offers some of the greatest benefits. Also, chaingrab = win.
Wow, that was way longer than I expected.