Unfortunately, "just a beep" does not say anything about the effect the collar has on your dog. One of the biggest points shock collar users make is to have the human try it out to see how 'harmless' it is. But that action only shows a human deciding their perceptions being more important than the dog's. And from a simple behavior perspective, that is not how any learning works in any animal. Besides the fact that dogs have different epidermal and nerve structures than we do, even if it was 'just' a beep or a tickle, we don't know how that dog will perceive that sensation.
A good analogy is situations surrounding human fear. If you were afraid of spiders, would it convince you to hold one if your friend reassured, "this one can't bite you - it's harmless!"? There is proof everywhere that just because a stimulus is literally harmless, doesn't speak to the psychological and physiological effects on the dog's mind and body.
I am sure that you love your dog and you just want her to be able to enjoy freedom and be safe. But objectively speaking, your dog is showing extreme signs of fear when this tool is applied. If you've only used the beep, then I can't even imagine how you would begin to desensitize her to the collar. I am not here to call you an abuser or torturer. But you have already identified the problem - this tool is not a good fit for your dog. Honestly, this is exactly how these collars work. The dog becomes too afraid of consequences to run away. Your dog is just having a more extreme reaction than other dogs might. Most owners would find this acceptable - if a dog is too scared to cross boundaries, they see the problem as fixed because the dog won't run away. I commend you for caring about your dog's emotions and mental wellbeing. And I understand that you don't want to see your dog cowering every time the device is put on. There are other solutions to keeping a dog safe and getting them exercise and enrichment outdoors. I hope you find a happy solution for yourself and your dog.