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.
I describe myself as a little dose of toxic masculinity.