Luckily, I too work for a large hospital where our pharmacy techs do all the mixing. They have to, we see sometimes upwards of 190 patients a day in our outpatient treatment center. We would never have time. The pharmacy also spikes the bags for us under the BSA and we backprime only by using a pump.
I agree with going and seeing the ONS information on safe handling. Have you ever had proper ONS training in your facility on safety?
Know how to safely handle these drugs and also how to safely deal with leaks/spills as well. Knowing what you should be doing will dramatically lessen your exposure.
Also, volunteer to be on a safety committee if you facility has one. You have the power to enact change and help protect yourself at the same time. Knowledge is power!