Beside the many great suggestions, you may want to take a look at some of the knife makers here on the forum, such as John at JK Knives and Scott at Gossman Knives, they have many choices for small fixed blades and if you don't see a style you like they will make almost anything you want at a reasonable price. Since I don't know what state your from I can only give you my perspective as a LEO in CA.
The fact that you have a CCW in CA does not automaticle allow you to carry a fixed blade concealed, here You can still be charged with a felony for the fixed blade knife even though you can carry a gun. It depends how the laws are worded. In CA " any instrument with or without a handgiard that is capable of ready use as a stabbing weapon that may inflict great bodily injury or death" is considered a concealed weapon. Fixed blades can only be carried exposed, and you are still subject to local ordanaces that prohibit it in public places. Generally a folder, other than autos are ok because they cannot be be used instantly to stab, ( and yes I know many out there will tell me that they can deploy the folder just as fast) but the law looks at it that way. A concealed fixed blade can be instantly used and is the what many get arrested for. So double check your local and state laws first. If you carry both the handgun and knife the handgun should be your primary defense weapon, it is what you are trained in, and can defend the use of in court, I.E.. Criminal and Civil trials.
The knife whether a folder or fixed should be a back up only when the handgun is present. Never refer to your knife as a weapon, it is for utility. Hope this helps, good luck on the search.