Agent Hill
Then there is reason to believe that the tesseract is not being completely discerning on who or what it brings through? If that is the case then I can understand your concerns and I would be willing to help. Would this be on a consulting basis or is this a more permanent job offer?
As an initial basis, there are a number of useful potions that do not use magical ingredients and I have been able to adapt several more to work without magical ingredients. However, it has not been common practice at home to use potions on Muggles so I cannot say whether they would have their stated effect, have no effect at all or possibly poison anyone who took them. That would need some research done, perhaps in conjunction with your chemists and doctors.
It should be possible to develop strategies for your agents should a Dark witch or wizard come through the tesseract. In regards to Occlumency, it should also be possible for strong minded individuals to be able to master the basics of that skill.