Skin mucus swab could be one of the least invasive method to get a good amount of DNA. Nevertheless, there is a risk of having microbial DNA contamination which could sometimes be of concern depending on the end use of the DNA.
Maybe a blood sample though caudal venipuncture? Probably works for medium to large round gobies (I assume this is the species you are working with still...?). The physiologists at the third floor at Zoologen can show you how to do it. I don't think a small fin clip will affect the fish much though, as long as you do not cut off the thicker fin rays at the edges of the fin - the fins can regenerate relatively quickly.
Thank you all for the answers. The fish are not big enough for buccal swab I believe. This is another species than the round goby (in theory) but about the same size. I'm familiar with caudal venipuncture and have performed it myself on sharks, and it might work with these fish.