If you have selected files in Copywhiz using the File Explorer (Windows Explorer), then go to the destination folder. Right-click inside the folder, choose Copywhiz → Paste Advanced to open the Copywhiz window and click on the 'Advanced Settings' button as shown in the picture below.
If you have Copywhiz's main window already open, then you can directly click on the 'Advanced Settings' button as shown in the picture below.
Now select the 'General' tab. The following window will appear.
Now, click on the drop-down as shown in the picture. Click on either, 'Skip' if you want to always skip when a file with the same name is found in the destination folder. If you do not want to always skip files, you can choose 'Skip if both files are identical' or 'Skip if destination file is newer' options also.
Press the OK button and click on the 'Paste Now' button to copy the files with the skip options enabled. A sound plays indicating the successful completion of a file copy task.