We usually prepare Prasadam for Perumal using jaggery. We do not use white sugar. In that case, on the day of Deepavali, can we make Bakshanams (snacks/sweets) using white sugar, maida flour, etc.? What items should be avoided? 

If it is not the custom in your household to prepare snacks for Perumal using white sugar, then prepare them without it. If you are accustomed to using it, you may prepare snacks with white sugar. Please follow your respective family customs. 
NOTE:
Making Prasadam with jaggery is considered very special/auspicious. However, there is no prohibition stating that white sugar should not be used. On certain days, white sugar must not be used. It must strictly be avoided on days like Dwadasi and Pithru days (Ancestral days such as Amavasya, the beginning of a Tamil month, and Shraddha). On other days and festival days, such as Deepavali and Sri Jayanthi, it has been the practice of elders to prepare snacks using white sugar.