Are Basenji's different from other breeds in this regard and are they sensitive to any of the anesthesia (sp?) vets use?
Yes, they are different.
Here is a previous discussion on this matter: http://www.basenjiforums.com/showthread.php?t=3401. There may be more if you do a Search.
Isoflurane is the preferred anesthetic. If your vet isn't familiar with treating sighthounds, Basenjis in particular, you might want to print out this information and take it with you. I would also recommend having a pre-surgery blood test done.