Hey kostask, is that anything like Meguiar's Heavy Cut Cleaner? They have several levels of them and honestly, I used to use that on table tops and anything that required the lacquer or whatever finish (poly or shellac) to be buffed to a high gloss. It was like a miracle! However, this guitar has a rather rough finish with parts of the finish being GONE altogether!! So you have to be careful what you use on it, because there is exposed wood.
To me the finish is kinda messed up anyway, so I'd probably use 0000 steel wool and go after it and see how it does. I mean, what's it going to do? Look BAD? Or just clean it and let it be. Unless you refinish, it's gonna be what it's gonna be, right?