No you don’t, whilst these are sensitive areas they don’t require a travel permit to travel for them:
Tibet Autonomous Region: Most people are aware that you can’t just waltz into Tibet whenever you want. A travel permit is required to enter Tibet and at this time is can only be issued through a travel group (more on this below). There is no independent travel in Tibet.
Parts of Xinjiang: Although the enforcement of this continues to change from year to year, historically travelers have needed a travel permit to travel the Karakoram Highway (the road from Kashgar to Pakistan) or to visit many of the ancient desert ruins in southern Xinjiang.
International Border Regions: Although technically not a “travel permit,” in order to approach any international border, you will be required to show proof of an ongoing visa to that country. The only exceptions here are borders where they issue a visa on arrival, such as the Kyrgyzstan border for most US citizens or UK citizens.
Whilst other areas may be sensitive, the rules are the rules and you are allowed 15 days in China without a visa as a Singaporean:
For less than 15 days of stay in China, Singapore ordinary passport holders are not required to apply for a visa.