I'd say it depends on which hike you want to do. If it's only one day, I don't think you need to train before going if you're reasonably fit and used to walking a few hours. For longer hikes, I would always prepare a bit. I did a 1-day hike through Shiratani Unsuikyo without any prior training. On a scale from 1 (walk in the park) to 5 (Mount Fuji), I would say Yakushima is maybe a 2.5. In summer it could be a 3 because of the heat, humidity and tons of insects, which made it more tiring than the terrain itself would have been. Hiking boots and long trousers/sleeves are essential (slippery ground, insects).