This sounds like a very tricky and potentially dangerous situation. A poorly socialised dog that has been used to being a guard dog and living outside is exactly the kind of dog who is most likely to bite. In my experience volunteering for a dog rescue, dogs from this kind of environment are most likely to cause problems for adopters, including biting. :-( H
Although it is true that neutered dogs tend to be less aggressive in general, in a dog that is poorly socialised with no experience of being a pet, who is showing some fearful behaviour, approaching him to apply a thundershirt or medication could be dangerous. Neutering is also thought to be a risk factor for making fearful/aggressive behaviour worse.
I would definitely not risk trying to take this dog out to a class, or trying to get a lead on him yet. If you feel you want professional help, hire a qualified behaviourist who has experience, for example rehabilitating guard dogs or working with rescue dogs that have been street dogs, who can give you one-to-one advice.
I can only suggest taking things very slowly, and feeding the dog very small regular meals. Don't make the dog come too close to you to get food, or he may come closer than he is comfortable with and then react in panic. Instead, leave the food and retreat, so that the dog can see you, but doesn't feel challenged.
Does he have a 'safe space' in the yard - a kennel or doghouse where he can feel safe? If not, and if you can provide one, that may help. He is feeling very insecure at the moment, and having a space that is just for him should help him feel safer. Don't approach him when he's in his safe space until you know each other much better and he seems much more relaxed.
Don't stare at him or make a loud noise, just be there, and provide food. Over time, this will develop positive associations around your presence.
There's a useful page here about working with fear aggressive dogs. http://fearfuldogs.com/key-concepts-of-working-with-fearful-dogs/
You might also find this book interesting : CHARLIE, THE DOG WHO CAME IN FROM THE WILD by Lisa Tenzin-Dolma. It's about an ex-feral dog, but Charlie did have some behaviour traits which sound comparable, and I know Lisa managed them successfully.
It sounds like this is a pretty difficult situation. Good luck. Please be careful.