Anything other than cotton balls saturated in saline can damage the cornea, and that would cause much more pain than she's experiencing now.
I can't think of why the pus should be so tough to wipe away unless it developed a dry skin, sort of like cooked pudding gets. Try pulling the cotton ball into two pieces. Using one piece, stretch it out so it's flat. Then wet it in the saline and fold it in half. Grasping the folded cotton, use it as a "grabber" and try to pinch the surface of the pus with the folded cotton and try to lift it off, as you would if it was pudding you are lifting the skin from.
If this works, it would then expose softer pus underneath that might wipe away. If not, use the cotton to pinch and grab and lift off the remaining pus.
This shouldn't harm the eye as cotton should be soft and silky enough that it shouldn't scratch the cornea.
Another thing that might help pull the pus off the eye is to use lubricating eye drops and squirt it under the pus as you are lifting it from the eye. The lubrication of the eye underneath the pus, if you can get the eye drops in there, should make it easier for the pus to come off the eye.
I am guessing that your lack of confidence in performing this operation is causing you not to exert enough force to the pus to get it to detach from the eye. Try to reassure yourself that this is necessary and you aren't doing anything that will cause injury, and the small increase in pain this causes won't be more than your hen can handle. Chickens are very brave about enduring pain, I'm sure you've heard.
To make this easier on you and your hen, wrap her securely burrito style in a bath towel so her wings are confined. This will give both of you a sense of security and make the task go much easier.