Nope.
You are attempting to find a technical solution to a human problem.
What you should do is to make pressure on your colleague to modify the web application to be W3C compliant and work with normal browsers.
Searching for workarounds would only make the problem grow: the web app would remain unusable outside IE, while growing over time, constantly hurting your company.
What if one day your company hires a person with a disability who can't use the app through IE?
What if Microsoft releases a version of IE which will break the compatibility with your app?
What if the person currently developing the web app leaves the company? Who would enjoy maintaining a web app which doesn't even care being compatible with any browser?
You (your company) lock yourself in a proprietary solution, and the worst one available on the market of browsers.
This is a mistake made by many companies a decade ago. The consequences were that those companies were not able to upgrade from IE 6 to anything else, and so would force their employees to use exclusively IE 6, forbidding any other browser.