"Ik draag de schoenen niet."
Translation:I am not wearing the shoes.
That is grammatically correct, but the meaning is different. Compare:
- Ik draag de schoenen niet - I do not wear the shoes
- Ik draag geen schoenen - I do not wear (any) shoes
In the first sentence, the speaker could be wearing a different pair of shoes. In the second, no shoes are worn at all.
No, I don't wear shoes is a general statement about not wearing any shoes ever (maybe you just prefer walking bare-feet), while I don't wear the shoes is a statement about a very specific pair of shoes (maybe they are a size too small). They are anything but close in meaning.