They’d probably have skipped the Gamecube since a stop gap console wouldn’t have been required.
I don't think anything would have changed with Nintendo adopting motion controls as they were looking for a new type of revolutionary controller before Dreamcast launched (looking for new revolutionary controller features is fairly regular for Nintendo, Gamecube remains the only Nintendo console without any notable advancement), but it didn’t materialize until the Wii. Nintendo would have still been introduced to the tech in the late N64 era, but on this timeline, the N64 will have the power and success to go a few years longer; so Nintendo could wait until 2004.
An earlier released Wii, without Nintendo getting the “Power doesn’t matter as much as you think” wake up call, would have been: A) more powerful, B) more expensive, and C) Probably uglier. So around the time of the original Wii launch we might see the Wii Lite model which would have the sleek approach the Wii did use. In another universe with a successful N64 and without a PSP, DS Lite would have just been “DS” launching in 2006 instead of being rushed to the market so quickly.
That's interesting angle. My line of thinking was that if N64CD was reality in that timeline, one of major things that leads to it would be that Nintendo realized they need to have better relationship with 3rd party publishers, thus giving them much better library and being much more competitive against PS. So, in the end, whether it's N64 victory or slight defeat against PS, standard "red ocean" approach would be more than enough for them to launch successor that is similar to N64CD - fairly powerful hardware that has same media storage as competition and brand name and good 3rd party support to carry it throughout generation.
So maybe in that timeline, Wiimotes come to well established GC as accessory to broaden the audience...
The way I see it is that Wii/GC, whatever it is called, wouldn’t have launched without a revolutionary controller. When the GC was launched, it was basically because the N64 failed and they needed something out to compete against the PS2. It was one of the few times Nintendo was reactionary, the other would have been the quick DS launch (which IMO, looked like an early model, while the DS Lite is really what they would have gone for). The GC was not a well thought out machine: first, it lacked the sort of controller advancement present in all other generations of Nintendo consoles, it didn’t play very well with some established Nintendo franchises and so we lost some franchises (like Street Fighter, which would have been on GC) and many others were simplified (especially combo-based games like SSX) with content and functionality taken out. Additionally, the discs were still too small for what was required - even Skies of Arcadia Legends had to lose some of its quality (audio) as a result, could bigger FF games have arrived on the console with proper storage? Especially post-Enix merger.
Any way. I figure that WiiGC console would launch later since Nintendo probably wouldn’t have to react against the Dreamcast or PS2 at that point: especially with Square, Capcom, Enix, and Konami as exclusives/near exclusive. Who knows? There’s even a good chance Nintendo would still have Rockstar North and Rare.
I think Gamecube/Wii launches in 2004 (or late 03) with a bit of an uglier model. 2006 Wii-Lite launches with DS (what we came to know as DS Lite in our timeline), and I also see it as being between Wii and Wii U power, HD capable.
One thing I forgot to mention was the Guitar Hero revolution would have occurred exclusively on Nintendo consoles instead of first on PS2, and then moving mainly to Wii (the Just Dance games, are to an extent, related to that).
I also think that while Nintendo did have issues with third parties, they would remain onboard because there would be no Square to lead them all astray as they did in real life... I’ll say Square was absolutely right to do so, Nintendo was HORRIBLE to them over the cartridge/CD disagreement.
Anyway, on the controller, Nintendo’s always been advancing their interface, sometimes for good or bad: NES brought the D-Pad, SNES brought the diamond face buttons and the shoulder buttons, Gameboy brought portability, N64 brought the analog stick, Virtual Boy brought VR. GBA and Gamecube were really the only only ones that didn’t try anything revolutionary. I think both were stopgaps that we’re premature, Gamecube because of the N64’s failure and strong competition, the GBA because the Gameboy was suddenly popular but they didn’t have the DS ready yet and GBC tech was WAY behind. In this timeline, GBA would still be a stopgap, but with a longer lifespan due to the fact that no PSP means Nintendo can wait, but the opposite would be true for GC/Wii, Nintendo instead has their home console in need of a premature launch - this the 03/04 Wii/GC launch with ugly controllers and perhaps a bulkier box.