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...