You mention Captain Falcon, but it's strange that you haven't made the connection that since Sakurai's made a Kamen Rider-esque style for Falcon out of the blue (which totally conflicts with his in-game portrayal in the F-Zero franchise where he's stoic and lets racing do the talking as opposed to punching someone in the face with a bird-shaped flame), he could easily make a combat medic style for Doc if he so chose.
Though if we're talking strictly material from the Dr. Mario franchise, there's always virus jars he can use to infect opponents with (such a concept can be chained to Megavitamins causing more damage/knockback if at least one end is the same color as the Virus that's ailing the opponent while curing them), and, a concept that initially though about for Doc when I first saw him on the Melee website years ago (the US one) that he'd actually
hit people with giant pills as melee weapons, not just throw them. (The little mini-clip had Doc bounce a Megavitamin against a wall to have it bounce and hit the opponent behind him while kicking them, making it look like he grabbed a Megavitamin and backhanded them with it in my 10-year old eyes)
In a way, this can help change up some of the standard attacks (though my medical instrument concept was directed at that anyway), though can help keep him somewhat similar to Mario while still being visibly different.
There's also half-Megavitamins (which I just refer to as "Megatablets") which are used as means to "attack" opponents in multiplayer mode when you score combos and impede virus-busting progress for them.
(Player 2's screen has an example)
Not for standard attacks, but if we're not going the medical instruments route (which I mainly was using in support of standard moves and in the case of the blood pressure meter, grabs), using these as means of combat are also viable, though it may be difficult to separate the function as compared to the standard Megavitamin toss.
I
did come up with an idea, though inspired by the New Super Mario Bros. games, in that Dr. Mario can copy Fire/Ice/Gold/etc. Mario's Spin Jump technique and toss two "Megatablets" to the sides of him like they do Fireballs/Iceballs/Gold Fireballs, etc. that isn't present in Smash for either Mario or Luigi.
Dr. Luigi also came up with some things;
namely the L-Vitamins for a wider projectile range, or for melee combat purposes (like my earlier idea; in fact, the L-Vitamins would be
better for that than the standard pills) and the randomizer (what multiplayer combos do to the opponent in Dr. Luigi; instead of dropping "Megatablets", their next L-Vitamin randomly shifts colors to change their strategies) which would be difficult to incorporate into Smash unless it instead randomizes
controls temporarily, a currently unseen function in Smash.
And though the Super Mario-Kun manga is not canon to the Mario franchise, when Mario was randomly turned into Dr. Mario in one comic, he was able to use a Koopa Shell attached with Megavitamin-shaped rocket boosters. That however.....
probably should be ignored.
The stethoscope idea is still viable, though.
After finals are over, I'll stop being lazy and finish up a full moveset for Doc that is semi-cloned (since I don't see any real reason to completely de-clone him) and we'll see how that goes.