Don't create a dead zone
Assuming you allow both horizontal and vertical swipes and only horizontal and vertical swipes then I see no reason not to simply say that if your swipe is within 45° of horizontal treat as a horizontal swipe and within 45° of vertical, treat it as a vertical swipe.
I'm not sure there a need for a dead zone on the middle where it gets treated as neither.
If the user actually does a 45° swipe (or close to it) then yes it is luck of the draw which happens, but I don't actually see that as a problem.
It seems perfectly normal behaviour and it's what I see happening on the Pulse and BBC news apps on my Android phone.
I think a dead zone would just be confusing to some users. Limit it to horizontal and vertical, and don't add another dimension by introducing a no-op as the third way.
Prioritizing the split
If you look at the tweet stream on Twitter for Android, they prioritize the most common or most useful swipe direction. (If you are roughly within about 10 of horizontal then it shows you the tweet in more detail on another page, whereas if you are roughly within 80 degrees of vertical then you scroll up or down in the stream of tweets.
Note that the preference towards the vertical swipe could also be an attempt to cater for the lazier swipe - perhaps one using the arc of the thumb when holding the phone in one hand.
So that's one available option if you are worried about users accidentally doing the horizontal action by mistake.
However, I think the narrow angle required by Twitter for Android is slightly too narrow as it slightly hinders discoverability by users who are expecting the 45° equal split.
Note that even through Twitter prioritizes the split towards the vertical, there is still no dead zone.