I think the key point you mention is that she is a strong empath. It isn't just a question of handling emotions or death, but as you've identifed a question of could your raw emotions spoil her authentic reaction.
If your reaction is stronger than her instinctual one, she might feel guilty. Or she could stay confused about whether her reaction is her own or just her feeling your reaction. Growing up highly empathic, I have a number of emotional memories that I can't determine whether I was reacting to a situation or reacting to others' reactions.
Personally, I would say get the raw primal reaction out of your system and approach her once that has levelled. Certainly don't hide the emotion, but do time your emotional state.
