I'm on the side of not bothering his wife. It's been a year since your ex-friend died, so maybe she has already moved on. Or she could still be battling with grief. Or she has moved on, but it would hurt her to revisit her husband's memories (even more so since these probably won't be happy ones). My advice would be to talk to friends or go to therapy to learn how to deal with those unresolved feelings (after all, life is messy and closure is a rare thing).
Still, if you really want to talk to his wife, the least painful way to do this is by putting the ball fully in her corner. Send her one message with the following : offer your condolences, how sorry you were to hear the news, and if she's up for it you'd love to talk to her about her husband. Be very clear that she doesn't need to, that she's free to refuse. If she doesn't answer back, don't send another message. If she starts to talk to you but at one point decides she can't or won't anymore, respect that. I understand you're grieving yourself, but it doesn't allow you to demand answers from anyone, least of all a widow. So if you decide to contact her, keep in mind she has the right to start this conversation or not, and to end it at any point, without getting anymore grief from you.
As a final note : talking to his wife might not offer you the closure you want. I lost my father after not seeing him for 25 years (I was six when I last saw him). I got to meet some of his friends, and I just got more questions and frustration out of this. Learning to let go will allow you to be at peace with this and have the added bonus of not bothering (at the least, at the worst hurt) a widow.