It is a personal decision with no wrong answer.
I am usually there for my animal's crossings. There was one where my horse was at New Bolton and I had to make the decision over the phone. This was back in the days before cell phones and I was a sales rep, so I had to make the call from a grocery store and I was crying so hard I could barely get the words out. The most important thing is that his suffering ended as quickly and quietly as possible.
I have been there for 2 horse crossings. Both have been quiet and pretty drama free. Even though I understand and am comfortable with the logic behind the process, I still sob each and every time. My vets have all been understanding about this. I think if you tend to be a hysterical cryer, maybe being there is not the best option.
I would suggest if you are not going to bury on your property, have the livestock person ready to pick up. When we had to euth my mare unexpectedly, it was around 6 hours before they were able to take her body. Because of our farm layout, I had to walk past that tarp multiple times that day and that was really hard.
(((((((hugs))))))) to you for doing what is right for your friend. You will be in my thoughts and prayers.

