I was/am blood gut queasy too. I’m still getting over it.
The way I’m getting over it is to take it slow. I only skinned my first squirrel, I didn’t gut it and make it food. My second squirrel I gutted and cooked. Both times I wore surgical gloves and I put about an hour between killing it and working with the body. That separation of time allowed me to start thinking of it as an object and not a living thing. Which of course is contrary to rewilding philosophy, and I hope I can slowly work this mental block out of the process. For now I work around it. More immediately, the next time I intend to use no gloves and just get my hands bloody.
In general, the way to get over a fear is to gradually expose yourself to that fear in small, manageable doses. It should always be a little beyond your comfort zome, making you a little queasy, but never so strong as to make you truly panic, which would reinforce negative associations and be counter-productive. After several exposures at that level you should no longer have as strong a reaction, and you can proceed to a stronger stimulus.