It won't cause an extreme amount of stress to move him as long as you do it gently and make it as quick as possible. You could put him in a smaller container with plenty of substrate and covered sides to make him feel more secure. As for being scared and hiding, that's just what the frogs do. Mine still ducks under the water every time I walk by after 2 years and it gets very minimal handling and most often will be fed if I'm coming close to the tank. Just follow the care guidelines closely and your frog should be happy.