Fish contains Omega-3 fatty acids that are one of the "good fats" and are "heart protective". Fish oil does not contain "good cholesterol", however. All animals produce cholesterol and we absorb some of that cholesterol when we eat the meat. This "dietary cholesterol" we eat accounts for a very small amount of the cholesterol floating through our arteries - maybe 1-5% of our total. Our bodies produce what people call "good cholesterol" (HDL) and "bad cholesterol" (LDL), and these are actually lipoproteins. Lipoproteins carry cholesterol around the body - HDL carries cholesterol back to the liver so it can be destroyed or recycled and LDL carries cholesterol away from the liver. Anyway, we do not eat "good" or "bad" cholesterol.
The skin of virtually all animals has more fat deposits than other areas of the body. This does not mean that the skin has more cholesterol, however. Also, you need to stop thinking of fish skin and fish oil as the same as chicken skin and fat. Fish fat (oil) is good for you and chicken fat is bad for you. Fish oil is an unsaturated fat (good fat) and chicken fat is a saturated fat (bad fat). Saturated fats come from all animals except fish and cause our bodies to increase production of cholesterol and LDL. Unsaturated fats from plants (olive oil, canola oil, etc.) and from fish (Omega-3) can decrease Triglycerides and may increase HDL in certain situations.
In summary; fish is good and we do not eat "good" or "bad" cholesterol, but we do eat "good" and "bad" fats. Bad fats can increase our "bad cholesterol" and good fats are good and sometimes increase our "good cholesterol" (but not always in every person - but they are almost always good for us anyway).
I hope this helps.