Deleting the template.xsnn from the form library will definitely cause problems and not solve this issue.
The form library needs a form template (XSN) in it if it's going to open the existing forms (XML). Removing the XSN will not remove the New button - it'll just give the user some odd error message if they click New.
Plus removing the XSN will also prevent users from opening forms in that library, since there's no form template associated with the library.
Then (to make things even more complex) every time the doctype is saved from DAT, DBXL will push the XSN back into the form library.
I think the solution is to simply not have a SharePoint mapping, and not have a form library. The dashboard idea might be just what you need.