I have a custom list and when I view a single item the standard
DispForm.aspx is used to display the item
I am able to override those fields via JSLink but is it possible to override the table itself and replace it with some custom divs?
Yes, that is possible to achieve using JSLink and display templates. Take a look at the following resources:
Some Client Side Rendering examples here: https://code.msdn.microsoft.com/office/Client-side-rendering-code-a52cf8a7
Customizing SharePoint forms: http://www.codeproject.com/Articles/223431/Custom-SharePoint-List-Forms
Hope this helps.