Okay. As a professional writer for over 50-years, I believe I know what you are looking for. Yes, he is quite likely to have blood on him and it would be readily noticeable. Unless he has carefully washed his hands or worn exam gloves during the process, he is going to have bloody hands and forearms because the body cavity is like full of blood. I can't think of a single instance, no matter where a deer is shot (I have killed over 400), that was completely devoid of blood regardless of the equipment used. The gutting process alone produces considerable blood. many of us wear disposable exam and or AI-shoulder length gloves. You can field dress a deer and be bloo stain free. However, it is dang hard to do.

Most likely areas for blood stains would be: hands and forearms, pants legs, shirt sleeves, especially the cuffs and boots. If he attempts to removed said stains, consider this. A man has bloody hands. A fly or mosquito lands on his cheek. he swipes at it, thus depositing a blood smear on his cheek of which he is unaware.

As for the field dressing or gutting process, the body cavity iis opened from sternum through pelvic bone. Care is take not to cut the innards but it is bloody anyway. Basically, eveything inside is removed. That's it.