Wood, Paper, Textile, Flammable liquid and Electrical fire are the most common type of fires that occur in home. Dry Powder Fire extinguisher offer the best fire protection coverage for your home. Dry powder extinguisher is the most versatile against most ranges of fire, for cooking oil & fats fire, more often than not, you just need to cover the pot with the lid. Dry powder can still help to reduce the fire but may not be super effective as compared to the wet chemical type. In fact, SCDF also recommends dry powder or carbon dioxide for home usage.
Below is extracted from SCDF website on procedure for dealing with kitchen fire. You can also see that they still recommend to use a dry powder fire extinguisher after trying out covering the wok/cookware.