A shader would be your best bet if you are already able to work with that and if slick does support shaders.
You could render your scene onto a FBO and use that fbo in the shader to mix the background and the character according to your idea of a cloak effect.
(research perlin noise in glsl, color blending basics and refraction)
If you do not know how to implement a basic passthrough shader that renders a texture, then you should take a step back and learn how to use shaders and opengl first, ThinMatrix has some very good beginner tutorials for the basics of opengl with lwjgl on youtube.
Pixel manipulation is slow, but that would work for a few textures per frame, it won’t give you refraction and custom blending though.
An easy way is to pre bake the sprites cloaked form, this is a huge workload though and changes will be tedious.