Is she like this under all circumstances or only when she is comfortable and doesn't want to be disturbed? It's not unusual at all for a Basenji to snark when they are comfortable, whether or not you surprise them. Some of mine, including my current boy, have been like that, some not. But just picking them up, say from the floor, when they are active has never garnered that response from any of mine.
When my current boy is comfortable, if I want to pick him up or move him for some reason, I find it is generally easy to finesse it by sitting next to him, patting him, and easing my way into picking him up. Usually that avoids snarks. However, if he does object I just go ahead and pick him up anyway, while chastising him verbally about his lack of manners. With an attempted nip, I will offer my hand under his nose and ask if he really wants to be doing that, which tends to end his little display. IMO, it is a mistake to allow the dog to back you off. You are teaching her that her behaviour gets her what she wants…....to be left alone and not picked up.......and the next time if you insist, she may escalate and actually nip. Better to avoid the situation entirely than let the dog learn her bad behaviour is rewarding. If you know your dog doesn't like being picked up, as Chealsie508 stated, you can certainly train her to be more accepting, but in the meantime try to avoid an incident that will make things worse.
Funny story. My show bitch didn't like having her toenails trimmed. You could see from her expression that she was getting increasingly annoyed, until finally she would utter a frustrated "aarrh", and grab my hand in slow motion. She never bit down, and the whole thing was hilarious. Many Basenjis just want to express their displeasure. The trick is to know the dog well enough to know if they are seriously threatening, or just voicing their "opinion".