I've read many times that Basenji's in particular "wake up badly". But then again- if you're cozy sleeping, who wants to be thrown off the bed suddenly? I don't!! 
Our Basenji has never bitten when we try to move her, but she does give a grunt. It's ALWAYS best to "ask her" to get down. Sometimes it takes her long than I want and I have to ask a couple of times in a row after she gives me that , "Are you serious?!" look, but she will eventually get down. You have to be really considerate and respectful about this one- I've read countless accounts of owners nudging the dog off and then getting bitten and they can't seem to figure out why… Duh. Treat others (including dogs) how you'd want to be treated.
As far as the biting thing goes- many Basenji's have the "I'm all that and then some" attitude. I find it commical. They are such a tough dog in a small, cute little package. I know what you mean about a little dog scaring you though. When Lexi was younger, she did NOT like my boyfriend at the time. At all. One time he took her out and she went potty. Immediately after that, he came in and got the clothes out of the dryer and took them and threw them on the bed to fold. Lexi runs right up on top of the bed and gets on top of the clothes. She looked him straight in the eye and pee'd on the clothes! OMG, my ex BF got SOOOOOOO mad. It was so obvious how intentional that was- she was definitely sending him a "This is what I think of you" message. He was so mad that he lunged at her and grabbed her up (I knew this wasn't going to be pretty! You just don't move like that around Basenji's- or any dog really). Lexi retaliated and bit the stew out of his hand. I mean, a huge chunk of his hand- it was amazing what that little dog could do. He of course dropped her and then she ran right over to me like, "Mommy! Help me!" It just wasn't a good situation. That was the only time she's ever bitten anyone ever. (PS- We have since married a fantastic man, in case you were wondering. )
The first thing I noticed about your post was that your puppy is REALLY young. Most puppies aren't let go until at least 8 weeks, if not longer. I also wonder if your puppy is okay health wise. Perhaps his tummy hurts and by picking him up, it's uncomfortable? Does he yelp in pain or is he just grouchy? I would definitely return to the breeder and get advice or see if she's had any problems with this from the parents or any of the other puppies. Do you know how much human interaction the puppies got while still with the mother?
I still think of Lexi as a shark from that movie Deep Blue Sea (horrible movie, but)-- she will try and test the waters. She wants to know exaclty how far she can go and still get away with something. They will get away with as much as they can- just like a kid. Little rascals! Hence all the posts about out-witting them!! However, aggression on their part (or yours) should not be tolerated. If you think he's being aggressive in response to HOW your handling him, then perhaps you can change your method and get him to trust you more and want to do the things you ask. This is not intended to offend you, but does he generally like you? I mean, does he sleep by you and want to play and be with you otherwise? Most Basenji's want to be with 'their pack'....
Seems like if he's okay in those areas, there might be something with the approach or the physical part of being picked up or leashed that he doesn't like. Anything scarey he's encountered outside that would make him not want to go out there?
Hmmm... Give us some more details.
