The Enterprise crew dealing with your death would involve:
Jonathan Archer: Handles it professionally around the others. He’s the Captain; he’s not supposed to openly grieve. Stay strong for the crew. Save the anger and sadness for when he’s alone. But for a while after your death, Archer noticeably mopes a lot. Isn’t as friendly or open as usual. Barely speaks to anyone other than T’Pol or Trip. It’ll take something big to snap him out of his grumpy moping, but that doesn’t mean he’ll ever forgive himself for letting you die
T’Pol: She is Vulcan. Don’t expect her to visibly show any signs of grief. But that doesn’t mean she doesn’t feel anything. A loss of a companion can be felt by any species; even one that has no feelings. She knows there’ll be a definite loss to the crew with you gone, and it’ll take time for her to get accustomed to your absence.
Trip Tucker: Is equal parts angry and sad. Trip is definitely a firecracker of emotions and he’ll switch back and forth between the two, depending on the situation. There’ll be times where he tries to act professional for the sake of others, but that doesn’t last very long. So he’ll end up snapping at someone or letting out a few tears alone in his quarters when he remembers something you used to do
Malcolm Reed: He’s more successful in staying professional. Pushing any feelings he might have to the back of his head because he knows you died doing your duty. That’s not to say he’s not sad, because he is. You were a good friend and Malcolm doesn’t have many good friends. But he’s better at compartmentalizing things like this.
Hoshi Sato: Will openly cry at the funeral, but she’ll be the one who goes around to her friends in the coming days and checks to makes sure they’re all okay. She’ll probably be the most stable and emotionally-available afterwards because of who she is, as a person. Telling everybody about the good times and such.
Travis Mayweather: He’ll probably cry here and there. Travis is definitely pretty open and feeling. Loves his friends and the family he’s made on Enterprise. So having one of them die would extremely sadden the small cinnamon roll. But I also think he’ll bounce back very quickly, turning your death into a reason to remember all the fun you both used to have. Travis is always the one who starts telling stories about you
Phlox: Tries his best to keep a certain professionalism. You’re certainly not the first patient he’s ever lost, and you won’t be the last. But this is different. There was more than just camaraderie between you. Like the others, you were family. You meant something to Phlox. And losing you would just make him feel sad and guilty