O. K. I see a couple of things in your post. How much does she weigh? I ask because although Basenjis can be difficult on leash and are strong dogs, they sure can't pull me where I don't want to go! If control is an issue, I find a martingale collar with a wide neck works well. However, it would be much better to find a solution to this problem. Have a look at this [video].https://www.youtube.com/watch?v=HwNe5COoGhk
Different breed, but I was very impressed with how well this guy's approach worked. Could be something worth trying if you have the patience for it.
You say she won't bite you. So what about her feet? Can't you just insist gently that she let you handle them, and reward with treats for cooperation? What does she do, specifically, if you try to hold them? I used to trim my dogs' nails with the dog upside down on my lap, and it worked for all of mine, not that they loved the process, but sometimes you just have to say "yes, I am the boss of you, get over it!" 😉