By 'actual fish' I assume you mean something like a piece of fresh fish?
There are some types of fish that are best kept to treats; perhaps most notably tuna, due to mercury content. That's not to say that a small amount of tuna every now again is 'bad', it just wouldn't be something that I, personally, would feel comfortable feeding on the regular. Mercury content will vary depending on where the fish was caught, but it's something to be aware of nonetheless.
Generally speaking, all fish commonly available on the market are safe to feed to hedgehogs. i.e salmon, whitefish, sardines, cod, mackerel, trout, etc. Obviously, there are toxic species - to both humans and pets haha. There are also some fish that I just wouldn't bother feeding (eel, farmed salmon, stuff like that). If you have a particular fish in mind and you aren't sure if its safe, you could always post it to double check.