Before I had direct family contact with diabetes, I had several diabetic friends. With my current knowledge, I now know exactly what they were doing, when they were testing - but in the past, all I was aware of was that John/Jane or whoever, got something out of a little case, did something quickly and then muttered something like "that's fine" to themselves and conversation and life continued. In other words, unless someone deliberately holds a bloodied finger in your face (as if you would!), there is nothing to see and nothing to get upset about. I would just carry on, discretely.
My only hesitation in saying the above, is that you say you work in a mental health facility, which could mean many things. If you are in circumstances where very sensitive and disturbed people might be over curious, there might just be reasons to test elsewhere. I can't advise on your personal safety, not having T1 experience.
Sally