Hello AlphaKilo10
Welcome to the SBB Community.
You can find information about travel with a bike on the IR95 (or generally on SBB trains) here:
https://www.sbb.ch/en/travel-information/individual-needs/travelling-with-bikes.html
You can find information about the travel with a bike on the R43 here:
https://www.matterhorngotthardbahn.ch/en/stories/mountainbike
As you will find out, bike space reservations are only possible on IC and EC trains. The transportation of bicycles is possible when capacity permits. On trains where a reservation is not possible, there is no guarantee for bike transportation, whatsoever.
But yes, since you start the journey at GVA, or GEAP in SBB terms, there should be sufficient bike spaces available as the majority gets on at Geneva main station, although the bike spaces are located in the last coach (the so called ‘FA’ coach) at the rear of the train, while the 1st class coaches are at the front.
And, since you only arrive midday in Brig, R43 will not be an issue either; of course, the morning and evenings are a different story.
Kind regards,
Roland