You can't just bring Stun Gun or Pepper spray on Singapore streets

Stun Gun or Pepper spray are arms which are used for self-defence in some countries, e.g. USA which can be commonly found in weapon stores. In Singapore, you see a different picture. Basically, you would not find a weapon store anywhere in Singapore (except for authorized shop for sports shooting) that sell arms or weapon that causes bodily harm.

Source: SmartStun Blog

Perhaps because Singapore has been recognized as one of the world safest city and the government finds bringing these weapons will only disturb the order.

Possessing, import or exporting of any of these Stun Guns shall be liable for a fine not exceeding $10,000 and imprisonment term extend up to 3 years.
 
For tourists, my suggestion, it would be the best to check with your travel agent what arms are not allowed to bring into Singapore as most of the arms are prohibited. Even toy guns are prohibited.

Reference(s)
1. Arms and Explosives Act (Chapter 13) Revised Edition 2003