The biggest problem here might not be the predator/prey issue, but that all reptiles are potential carriers of salmonella which is deadly to birds and it's not great for humans either. The info at
http://www.petplace.com/reptiles/salmon ... page1.aspx says it's possible to test reptiles for salmonella but the test isn't 100% accurate. If the lizard is diagnosed with salmonella it can be treated with antibiotics, but it's basically not possible to eliminate all the bacteria.
The risks of cross-infection will be reduced if you wash your hands between handling the skink and the bird, and avoid putting the skink in places where the bird is likely to be later.
If you think that looking at Chasca truly helps Boniface relax, it's probably safe enough to let him look from a distance. But birds sometimes become very quiet and still when they think a predator is nearby, hoping that the predator won't notice them. My guys do this a lot when they see a hawk out the window. Pet birds aren't always as predator-savvy as they should be, so maybe Boniface really isn't afraid of Chasca, and maybe he even has previous experience with lizards and likes them. But just consider the possibility that maybe relaxation isn't really what's going on. If Boniface makes little soft "beep" sounds while he's looking at Chasca, that's the way cockatiels quietly tell each other there's a predator in the area.