What shoes for trekking/hiking on backpacking trip?

Hello! I am spending a month in Vietnam this December after two months in Thailand, Laos and Cambodia. My rough plan involves a few multi-day treks, and weather permitting I'd really like to summit Mount Fansipan. Would this (and other Sa Pa trekking) be doable in sturdy waterproof hiking shoes? Or do I need to bite the bullet and take hiking boots for my three month trip? Any footwear recommendations appreciated!