Personally I've only found a few types of shoes that fit my twins' thick feet without pinching their legs. These slip-ons are very easy to put on and really just slip on. Material is thick, definitely water repellent, haven't tested if they are waterproof (doubtful) and feels very durable.
Stride Rite Athletic Running Shoes for Little Boys: Enhance Performance and Comfort
54 Review
Okilol Toddler Sneakers: Athletic π Running Shoes for Boys with Style
61 Review
π Winter Walking Sneakers: Infant Toddler Boys' Shoes for a Stylish Yet Cozy Adventure
60 Review
TOEDNNQI Sneakers: Lightweight Breathable Athletic Boys' Shoes and Sneakers for Active Performance
55 Review
HOBIBEAR Lightweight Athletic Sneakers For Kids - Perfect For Running, Walking, And Sports!
10 Review
π Highly Durable Kids Running Shoes - WETIKE Boys Basketball Shoes Non-Slip Outdoor Trainers for Girls (Little Kid/Big Kid)
8 Review
Non-Slip PIZOFF Toddler Water Shoes: Quick-Drying Aqua Socks For Beach, Swimming, And Walking Adventures!
3 Review
Quick-Dry Closed-Toe Water Shoes For Boys & Girls - Ideal For Aquatic Sports - Toddlers & Kids Size - HOBIBEAR
51 Review