You could accomplish this by building a tool using the PythonAddins framework or the ArcObjects AddIns framework. I know that you stated you didn't want to use ArcObjects, but I feel that you'd probably prefer the AddIns framework over the COM component approach. Both the PythonAddins and ArcObjects AddIns routes will create a file which the user can install on their machine without any administrative privileges.
What is a Python add-in?
http://desktop.arcgis.com/en/desktop/latest/guide-books/python-addins/what-is-a-python-add-in.htm
Creating a Python add-in tool
http://desktop.arcgis.com/en/desktop/latest/guide-books/python-addins/creating-an-add-in-tool.htm
Building add-ins for ArcGIS for Desktop (ArcObjects)
Walkthrough: Building custom UI elements using add-ins