Yes, you can do Wazifa without Wudu. Wudu is not strictly necessary for all types of Wazifa. For example, non-Quranic Wazifa. You do not need to be in Wudu to do these Wazifas, but I always recommend having Wudu because it helps you stay clean and focus better. However, if you can not perform Wudu, it is ok you can still do Wazifa without Wudu because your tongue is clean, and the most important thing is to do Wazifa with full sincerity. When you are reciting Wazifa from Quranic Ayat, then do Wudu before starting the Wazifa.

One evening, my friend Sara felt very worried about her exam the next day. She asked me about a dua for success in exam results. Sara was unsure whether she needed Wudu to perform it so she called me.
Then I sent her this link to clarify whether Wudu is required for the Wazifa or not. Thank you Akhtar Bhai your help is always appreciated.