We are lucky in our breed to have a pedigree database that has nearly every Basenji that has been bred in the world, so I can actually trace mine right back to the original dogs that were brought in from Africa.
It is partly true about basenjis not barking but they can give a one off single cough type bark. Like someone else said they are far from being mute especially if you have more than one as they can start each other off. One of mine will sing to you if so ask him lol.
How about a Norwegian Buhund? I was brought up with them and we have bred a few that have gone on to actually do the job they were intended to do very well. Not sure how common they are in your neck of the woods though.
I have had the pleasure in meeting Gunner & Helena and a couple of their dogs. Sadly Gunner passed away a couple of weeks ago so my sympathies go to his family at this hard time.