I cannot comment on Machu Picchu specifically, but google gives the height as just under 2.5km. Two years ago I was in the French Alps in the summer and took the ski lift to the top meadows and these were just over 2.5km. I was using the older Accu Check Combo then rather than the Insight but all was fine.
BTW I fly every three months or so long haul and I never disconnect for take off or landing.
I have not hiked like your planning, but have done intensive white water multi day kayaking trips where for a for a day or so I did not need any insulin. If it was me I'd reduce my basal (by around 30%) a few hours before I start the hike and then test every hour or so and adjust my basal as needed, as I have a CGM so its easier for me to see what impact the hike is having in almost real time.