I don't necessarily agree. Erika, you say you haven't seen him since you were four - but is that twenty years ago or fifty? He's your second cousin - if I understand cousinships correctly, that's not very far removed. Are there other family members who are closer to him who could drop a hint (especially if one of them has read your work.)?
From what I've read of your posts, I know you can write very well, so you have nothing to be ashamed of or fearful that your cousin would turn up his nose (unless he's writing books 180 degrees away from yours.) I say, go for it and try to set up at least the opportunity to ask him. You may be very pleasantly surprised at the outcome. (I was, I asked a college professor I'd never met to review one of my WIP's and he said yes immediately and loved my book.) Why don't you bite the bullet, call him and set up having coffee (be honest, tell him you're working on a book and would love to have some of his insights), tell him about your book, and give him to opportunity to offer to look at it - and if he doesn't, ask him if he'd have time to look at a chapter. My adage - nothing ventured, nothing gained. Puma