The letter is a good idea. This way it won't seem like you're asking for an answer right away, and they can talk about it.
Going to him first... honestly, I would take it pretty personally if someone told my husband he liked me before he told me. It would feel like going to my father to ask for my hand before proposing to me. I don't belong to another person, and I can make my own decisions. Don't negotiate me like that before I'm even in the loop. I understand talking to your spouse before you talk to your person of interest (so, in your wife's case for instance, I do think she should talk to him first if she likes you) but talking to your person of interest's spouse before them doesn't sit comfortably with me at all.
That's why I suggested talking to both of them at once. And once again, I think Cat's suggestion of doing it in writing is a very good one.