I was thinking of the smaller primates, like tamarins, lemurs, marmosets, etc. Nothing even as large as a gibbon. You'd use the larger, and more closely related, species for the final testing, if required.
The 'sister' organization to the one I work for has successfully maintained a large number of primates, including; Baboons, Chimpanzees, Macaques, Marmosets and Tamarins.
Here are some of the big nasty Hannibal, Lector types
And here are some of the ones I was thinking of.