An anecdote: A friend once explained away an Emerson La Griffe as an expensive craft knife. Deniability is an asset.
For that matter, so is mundane utility. The more you use it - even if it's for opening your mail - the more comfortable you get with your draw and your grip, and it may even help with your confidence in a pinch, depending on your psychological makeup.
The Ka-bar and HK are much cheap thsn the Karambits, and are special purpose - designed to be used by work weak-side when you are carrying a gun on your strong side. Just like the Karambits, you need to understand their purpose and train in their use. The ka-bar and HK are designed for stabbing and straight forward movement, while Karambits are not designed for stabbing, and generally move in an arc. The Ka-bar and HK and some of the Karambits are belt knives, not pocket or jacket knives. You will need a jacket or other garment to conceal them.
Of all of these, the LaGriffe is the best for self defense.
Karambits have a forward facing tips just as much as these angled straight blades do. A thrust with a karambit is entirely consistent with throwing a punch.
And I disagree with the Lagriffe being the best choice for self defense.