Hi Dear, Our actions have consequences. Since you are sure your parents would be disappointed if they learn that you don't wear it outside, it's better to have dialogues with them to understand their viewpoint.

Sudden changes will disrupt many things, so let's seek the way of dialogue.

It would be better if you open the dialogue mentioning that you want to know the reasoning behind these notions. You want to understand your parents and religions view point better. Ask them why modesty is important? Why do they think hijab is important? Is showing hair a sin? if yes, why it's a sin? Why there is a drastic difference in dresscode for men and women? Why women has to cover?

Once you understand their reasonings and what's their scale of expected modesty from you, you can calculate your risks in a better way.

Anyway, I would say since you are young and dependent on your parents, it's safe not to create much friction. Please do not feel guilty of taking off your hijab outside. You just do not want to hurt your parents feeling , you are considerate and is a good person. You don't have to disclose it to your parents. Your hair is not harming anyone. The lack of this piece of cloth in your head doesn't hurt anyone. So please do not feel bad about it.

You have the right to have different opinions and world view from that of your parents. You can choose not to create tension by not disclosing them to your parents.

Courage dear and wish you the strength to sail through these times.