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"To run without saving" was the first idea I got, but it was difficult to pursue in first phase. After your hints I think I have achieved what you have described.
I have done a few fixes(luckily in a single file ScriptBinding.py) which are giving satisfactory result.
I am attaching the original, modified and the diff version of files named ScriptBindingOriginal.py, ScriptBinding.py and ScriptBinding.diff respectively. 
Here is what I am getting with the new code
Traceback (most recent call last):
 File "*Untitled*", line 3, in <module>
 File "*Untitled*", line 2, in f
ZeroDivisionError: division by zero
This is the summary of the patch (idle-python3.4)
+import io
....
#====== One member in class for reducing annoyance ====
 self.no_save = False
#====== New definition for function tabnanny======
- def tabnanny(self, filename):
+ def tabnanny(self, source):
+ f = io.StringIO(source)# , os.linesep *****Maybe*****
- with tokenize.open(filename) as f:
#====== Added 2 functions =========
 def source_from_file(self, filename):
 with open(filename, 'rb') as f:
 source = f.read()
 if b'\r' in source:
 source = source.replace(b'\r\n', b'\n')
 source = source.replace(b'\r', b'\n')
 if source and source[-1] != ord(b'\n'):
 source = source + b'\n'
 return source
 
 def source_from_editor(self):
 self.editwin.io.fixlastline()
 source = self.editwin.text.get("1.0", "end-1c")
 return source
#====== New definition for function checksyntax======
- def checksyntax(self, filename):
+ def checksyntax(self, source, filename):
#====== Changes in function run_module_event (Main) ==========
 def _run_module_event(self, event):
 filename = self.getfilename()
 filename = self.getfilename()
 if not filename:
 self.no_save = True
 source = self.source_from_editor()
 filename = self.editwin.top.wm_title()
 else:
 source = self.source_from_file(filename)
 self.no_save = False
 code = self.checksyntax(source, filename)
 if not code:
 return 'break'
 if not self.tabnanny(source):
 return 'break'
 interp = self.shell.interp
 if PyShell.use_subprocess:
 interp.restart_subprocess(with_cwd=False)
 if not self.no_save:
 ....
 interp.runcode(code)
 return 'break'
#====== Finally suppressing the annoyance ======
 if autosave and filename:
 self.editwin.io.save(None)
 elif self.no_save:
 filename = None
 else:
 confirm = self.ask_save_dialog()
Please have a review and let me know if it can solve this issue.