Hi Bridget
I think it would be a good idea to take walking boots on this tour (more than most) as you will be walking on some fairly difficult ground - at Machu Picchu there are quite a few high steps and a steep gradient, and I expect the walking in the Amazon will be fairly uneven too. When I went to Peru I was grateful to have some good support for my ankles.
If you are concerned about luggage space, you could consider wearing your walking boots on the flight out, so they wouldn't be part of your luggage allowance.
Kind regards,
Olly, your editor