I selected <NO> while installation.
I opted to not to provide root permission to wireshark but as I read further I got to know I will require root permissions for wireshark to work smoothly. I know I can still use wireshark with sudo but I don't want that. Removing and reinstalling wireshark doesn't works as whenever I reinstall again, it never asks for the permission again. What should I do ?
You made the right choice, see Running Wireshark As You, 'A better way' to setup your capture, as pointed to in the answer below.
On what operating system are you running Wireshark?