All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we thank and praise Allaah Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the Day you meet Him.
We advise you to seek beneficial knowledge and perform good deeds.
As regards wearing a cross, the scholars stated that it is not permissible for a Muslim to wear a ritual that is peculiar to the non-Muslims, as is the case of wearing a cross, because wearing it is imitating the non-Muslims in their disbelief, even if one does so outwardly only, and this is approving of the falsehood upon which the wrongdoers are.
We believe that you do not need to do that, however, if you fear that you will be harmed by showing your faith (becoming a Muslim), you have the right to conceal it on the condition that you abide by the religious rites in secret. If it is possible to show your religion, then do so and be proud of it and do not fear anyone except Allaah. This may be a reason for calling your parents to Islam and they may become Muslims thanks to you.
For more benefit, please refer to Fataawa 92413 and 106089.
With regard to the parents becoming unhappy, then this is an easy matter; parents may become sad just because of their children leaving them. Even so, their children may not give up the idea of leaving them if there is a need for that, like travelling and so forth, let alone if their becoming unhappy is due to religious reasons.
Allaah Knows best.