I just got my bow hunting license 2 years ago. Noone asked if I had proof of a hunters safety course. AS far as I know, the bow course is totally separate from the hunters safety course. You may have one and not the other. At all hunter's safety training courses I've helped with (rifle) there has always been "hands on" towards the end of the class. It teaches those taking the class how to operate a lever, bolt and semi auto action gun. (usually just the younger people taking it but occasionally you'll see a man or woman in the class that doesn't have much experience with the different actions) They are required to show safe handling and how to operate the safety on the gun. Then of course they get to shoot them. All are .22's and I will bring one of each style as well as the instructor and another volunteer. They do not allow the people taking the course to bring their own guns. No need really as they only shoot 5 rounds from each action. My bow course was the same but they encouraged people to bring the bow they will use. They provided bows for the rest. We took 3 shots as they only wanted to see you go through the motions with no issues. Anyways, I do not know of anyone that is requiring a hunters safety course completion before taking a bow course. A bow is not considered a firearm and it doesn't require a background check so even if someone is not allowed to legally own a gun, they can own a bow ... and now a crossbow.
To LEGALLY "hunt" with an air rifle, you must have taken a hunters safety course to get the license for small game season. You can't have a hunting license for any game(fish excluded LOL) unless you take the safety course. I've heard of people that are not able to buy a firearm, taking the hunters safety course and pellet guns are what they use. Of course they also go after the bow course as well and use the bow for big game. Taking somebody's right to hunt away is beyond gun ownership isn't it??
I'm also mostly vegetarian and I just make sure there is someone able to take the meat and if not, then I do the venison donation program through NYS. I think that's a really good program!! I do the same with small game as well .. I make a few calls to friends that will use the meat, and tell them that I'm going hunting and make sure they will take the game I get. If I can't get ahold of anyone, I'll just go out and bring a camera. I love the outdoors time, I like the time alone so I can think and just enjoy quietness (as long as the anxiety stays at bay for awhile and I don't go back home) ... but it's still the hunt I enjoy the most. Does this sound weird to anyone?? I feel like a wabbit slayer who only eats the carrots!!