Peru sounds like lots of jaw dropping sceneries, combined with colorful details around the people, like ponchos and blankets, city details etc. That requires a certain setup. If you add wildlife, the pack grows a lot. Since you don´t mention it, I drop it.
For most people photography is like golf. Everyone is practicing their hundreds of yards drives for hours, but the games are won on the putting greens. In photography that means everyone thinks they need big lenses (your 100-400mm), but 95% of your images will (most likely) be shot at less than 100mm (on an APS-C). If your friend is willing to carry the 100-400, let him do that and concentrate on the stuff below 100mm. I know I would. If you can´t afford to buy the right gear, rent it (How often will you be going to Peru?)
I also agree with neuroanatomist. It is much easier said than done to make spectacular wide angel shots. Get the 10-22 mm in time, with a circular polarizing filter and a tripod, and practice a lot before you go. I would also get the 85mm f1.8. It is (in my view) the best value for money prime carrying Canon´s name (I use the 85mm f1.2L II a lot, but on FF bodies). Portraits, shallow depth of field, sharpness, color, you name it, this lens delivers.
A different alternative you could think of was to get the 24-105 f4.0L IS. Optically this lens outperforms the others you have on your list and it is now sold for very acceptable prices. I use that a lot (but on a FF body). But with your APS-C body, you will need something in the wide angel area. The 10-22mm would solve that. For some shots there is no alternative, but for the wide sceneries, where nothing moves, you can stitch multiple pictures (requires the tripod) and make the need for a true wide angel lens less apparent. That is a fun and creative process (practice before you go), where you have to think before you shoot. It requires a tripod though.
Good luck with your selection! Peru is a great destination (which deserves the right stuff
Eldar