Even in a fantasy world with zero marine hazards (no sharks, jellyfish, pirates, rogue waves), an exercise ball fails as a transoceanic vehicle for fundamental physics reasons.
A 65-cm ball displaces ~140 L water → ~140 kg buoyant force. An 80 kg person + 2 kg ball = 82 kg. You float high — center of gravity above center of buoyancy. Result: extreme instability. You'll capsize instantly, repeatedly.
Walking on a sphere on water: your feet push tangent to the surface. Reaction force spins the ball — you stay in place (or rotate). No keel, no paddle, no sail = no net forward vector. You're a hamster in a wheel.
Ocean waves (even 0.5 m swell) impart orbital motion. The ball follows orbits — you go up/down/forward/back, net zero drift. Stokes drift might move you ~cm/min downwind — at that rate, Pacific crossing = 3,000 years.
Your body acts as a sail. Wind pushes you downwind — but the ball drifts faster (lower drag coefficient). You separate. Or you're dragged underwater if tethered.
Continuous balancing effort → exhaustion in minutes. Hypothermia (water ~15–25°C) in hours. Sleep impossible. Dehydration, sunburn, saltwater sores.
An exercise ball gives you buoyancy without stability, propulsion, shelter, or navigation. You'd drift, spin, capsize, and perish. The ocean doesn't negotiate with physics.