You've made an excellent approach and yes, the suggested relationship could be as you suspect but given the statistics, it is likely a second cousin. I have a half sibling in my project and the closeness of matches doesn't change alot once you get past first cousins. DNA is often a 'tool' to use in collaboration with paper research. In this case you can learn alot if the cousin will collaborate. Gedmatch will be an invaluable tool for further analysis and it will come back up. If you would find the cM comparisons helpful, I'd be happy to email directly from my own data of half cousin matches compared to full cousins.