I'm sorry, but I think the passenger list that shows his father as Wakim is for a different Nicolas Corey (at least if it's the one for the SS Paul sailing 25 Jan 1911, with Nicolas, age 21). There's a 2nd page to it that says he's going to stay with his brother Georges Corey at 297 1/2 Oak St, Lawrence, Mass. It also says Nicolas had previously lived in the US in Lawrence, MA from 1903-1909. The 1910 census shows a George Corey living at 293 Elm St, Lawrence, MA. The address is a little different, but I'm guessing this is that brother George (but the name is so common, it could even be another). There's a different household in the 1910 census that I believe is your family... they're living in Syracuse, and it's Mary with her sons: Nicolas, 23; George, 20; and Joseph, 18.
I wonder if you could find any death records for Nicolas or his brothers that might list their father... or maybe for Mary listing her spouse? I can't find those online, but you might be able to get them in person or by mail. Or marriage records for the boys also might list parents. And if you can find passenger lists for this Nicolas, that's a possibility. I'll keep looking online to see if I can find more.