May be following is a solution / workaround to your problem.
1.Add following line of code to the master page of your application
<meta http-equiv="X-UA-Compatible" content="IE=9">
This will open the page in IE 9 mode. You can check it by opening F12 developer tools and switching to Emulation tab
Note: This will only change the Document mode and not User agent string.
2.Now if you want to navigate to your application through a shortcut on desktop then there are two ways to do this
(a) Simple Way:
i. Set your application home page/start page as your IE home page (Internet Options-->Home Page)
ii. Create a copy of the existing IE shortcut
iii. Rename the shortcut as your application name and change the icon
(b) Better Way:
Problem with the first approach is whenever you open IE it will open your application start page as it is set to home page of IE.
So, create a small BAT file to do this.
i. Open Notepad
ii. Type following
start iexplore http://suvendugiri.wordpress.com
Note: Please replace the website name with your application start URL
iii. Save this file as YourApp.bat
iv. Right click on this file and go to "Send To"--> "Desktop(create shortcut)"
In case I am missing something please let me know.