A) Many Smash tournaments universally ban all controllers besides 1st party GameCube Controllers (GCCs).
By 1st party, I mean GCCs that were made by from the original producer - Nintendo - and not a 3rd party controller like those of GameStop, MadCatz, and others. So no, unfortunately, there aren't any GCCs made at a smaller size that are tournament viable, since 1st party GCCs only come in one size.
B) In all of my 10 or so years of playing Smash, I've never heard of a controller that works as reliably and lasts as long as the 1st party GCC.
3rd party GCCs have generally earned the reputation for wearing down and breaking much more easily (like in your case with your control stick), or for having awkward feeling buttons. Generally, 1st party GCCs don't start breaking down until years of use; even at the top levels of Smash play, where players with certain mains (e.g. Melee Captain Falcon) that require constant, intensive use of a particular few buttons (in this case control stick), it can last for at least several months to a year before breaking. If those guys were using 3rd party controllers, I guarantee you, they'd break in mere weeks, if even that long.
C) 1st party GCCs don't have any lights (e.g. LED lights that require batteries) by default.
Wavebirds (1st party wireless GCCs) are the only exception, which light up to show you that they're on, but all types of wireless controllers are usually banned from tournaments anyhow, due to a plethora of issues they present that could simply be avoided by using battery-less wired controllers.
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Also, just to clarify, the 1st party GCCs come in several colors. The most common and easily obtainable 1st party GCCs today are White, Jet (black), Indigo, Platinum (metallic gray), and Spice (orange). White GCCs are by no means the only "official" controller, but having been the only 1st party GCC to be produced using a more recently developed/upgraded model, they have a much longer cord, and are generally sturdier with longer-lasting buttons. Both are considered to be good changes, but many dislike the cord's cumbersome length (myself included), and the buttons are often stiffer than average. That is, due to their sturdier buttons, new White GCC buttons always feel noticeably stiff until "broken in" over the first few days/week after unboxing them. Even then, they're very slightly stiffer than regular GCCs, but that can easily be adjusted to, and seems to be a reasonable trade-off for a longer-lasting controller.
(There are other rarer 1st party GCC colors, too, but those can be absurdly hard to find and often considered expensive collector's items. If you're curious, you can check them out here. I'm sure some can be obtained more easily than others, or you might into a stranger or friend and realize they have one you can make a bargain for, so if one catches your eye, go for it aha.)
Good luck finding a new controller that works for you! (: