The BBP standard does not apply if the cells are not human (experimental animals are exempt if not deliberately infected with the HIV virus). I am guessing the mouse liver microsomes are not from mice deliberately infected with HIV--that'd be unusual for a chemist to work with--but I don't know where they're coming from....
SDS's for commercially prepared biological materials generally communicate the chemical hazards (are the tissues in formalin? are they in 0.1% sodium azide solution in RNAse-free water?) and are not designed to communicate biohazards. There are Canadian SDS's for infectious materials but they do not cover animal cells--which often are not known to be infectious (think of all the dog hair, slobber, etc many of us deal with daily).
There are excellent resources for biosafety practices, starting with the CDC BMBL--I'll put the link at the bottom. I don't know exactly what your faculty member is working with--are these commercially obtained or are they from a colleague doing toxicological studies,etc-- but she/he may want to talk with colleagues in your biology dept. From time to time I have posted questions to the ABSA biosafety listserv and have phoned/emailed the BSO (Biological Safety Officer) at a larger institution. They have always been helpful and patient. In addition, you may want to talk with Keene State's IACUC Chair--they can direct you/your faculty member to some appropriate resources.
BTW, the belief of less risky material when 'even if the [human] organelles come certified as free of viruses, etc' is, in many BSO opinions (and mine too) a lot of bunk. You can't economically test for all bloodborne diseases (think ZIka, West Nile virus) and that is what the OSHA BBP standard requires IF you are going to consider the biological material exempt from the standard. Not just checking for HIV and HepB (not to mention false negatives). It's great to have some negative test results--I wouldn't want someone who's not worked at BSL2 to suddenly work with HIV+ materials--but your safest course is to follow the BBP Universal Precautions no matter what the test results say..
Here's the link to the BMBL--oh, and you'll notice that safety glasses for BSL1 or BSL2 are required only sometimes: "Wear protective eyewear when conducting procedures that have the
potential to create splashes of microorganisms or other hazardous
materials..." Welcome to a Brave New World--they're gearing up for a new edition and I'm going to try to push for a greater emphasis on safety eyewear...
Good luck, let me know if you want anymore information about the biosafety listserv...