I will invite those with the training and experience to comment further.
OK
Not all people should carry a gun. This especially includes people who aren't comfortable with guns, and those who won't train to an exceptional level to where they would actually use the gun in a fight. To use a gun in a fight, most people need to see the fight coming from a ways off, they wouldn't know what to do if they had to draw the gun and fire at a moving target, or while they themselves were moving. Most firearm training is done NRA Bullseye style, with the shooter standing still, or in some IPSC stance, shooting at a stationary target, which does nothing to prepare the shooter to actually fight with a gun in the real world where attackers and defenders move or die. This includes most shooters, many here, of course
I spent a year getting my @$$ kicked in an exceptionally brutal family system of Kali. It turns out that a knife can be fine for self defense, as can a ball point pen, a shoe, a brick, a pipe, or any number of other items that we use and walk past day to day. Everyone, men and women (including those who carry guns) should know how to fight with or against sticks, knives, and bare hands. Anyone who doesn't know how to fight without a gun stands a good chance of being out done in a real fight, even if they have their gun.
I tell women (and men) that I care about to go train in Kali, Escrima, JKD, Win Chung, or any other realistic martial arts school in the area that understands that people in the real world have knives, and you'd better learn to fight with and against them. Sadly, most won't put forth the effort
If someone doesn't want to learn to fight with, and carry, a gun don't force it. Winning a debate won't instill the situational awareness, attitude, and skill needed to fight with a gun, or anything else.
OP, if your wife will learn to fight with the knife, awesome! Train her up! My wife carries the Boker Subclaw daily. It is small and flat and probably the best knife, for the task, that can be carried everywhere:
http://newgraham.com/store/product/4310/SUBCLAW-Satin-PE-BOK585/
My favorite small knife, by far, is the Spyderco Lava. I've started working in an office where a big knife would be a poblem. My Lava, with its 2" blade, isn't theatening to anyone, in apperance, but the handle allows for a very secure grip and the blade cuts like a bigger knife:
Both knives were designed by martial artist Chad Los Banos, who knows quite a bit about playing with knives.
Good luck training the wife