Never hide anything from your spouse.
Do explain to her that she would not have you if not for him saving your life. Tell her the details because she doesn't have a reference point for this.
Explain that this is as important to you as helping family in need and go over the family budget together to see if there's actually any room to help. If there isn't then don't beat yourself up over it. If you don't have the money you simply can not help him. OTOH, if you have a little "me money" in the budget and there's a smidge left over in the family budget, go ahead. Remember that your obligation to him is primarily yours and not your family's.
What you've not explained is what other reasons your wife might be opposed to you doing this. Does she think your friend doesn't manage his resources as well as you do and if he were a little more responsible he'd be able to handle this himself? Considering the expense associated with hunting is it really the most cost effective way to put food on the table or is it more of a way to balance the fact that he enjoys hunting? Your wife probably understands fully what it costs to feed a family on a tight budget and may not see the food issue from the same perspective as you and your friend. Be sure that there's a real need here and not a rationalization for the new gun.