In your case, you are really wanting UA sniffing because your QA team is testing on [let's say] Firefox and Internet Explorer and your business wants to disallow other browsers. However, you've probably read about all of the drawbacks of UA sniffing, the fact that browsers can spoof other browsers, difficulty in maintaining an up-to-date list, yadda yadda. Well thanks to npm you can have reliable and current UA sniffing and reconciliation via modules like useragent.
npm install useragent --save
If your QA team was actually testing features and your business rules were written by a reasonable and logical person, you could simply use feature detection like the rest of us. Instead, you're going to block users in 2016 from using your app/site because a naive project owner wants to only support browsers he/she is comfortable with (sigh).
Edit: If you really want to impress someone you can write functional tests which actually execute in the browser. You can automate the clicking of buttons/links, fill out forms, and write assertions against the side affects of these user actions. For example, you can fill out a signin form with invalid credentials, click submit, and expect the "Invalid login" error message to be displayed. Selenium is a very popular tool, but there are also free open source tools like FuncUnit and others which allow you to do this. Then you can use things like browserstack to run these tests in the browsers of your choice. There are also free tools like Testee which allow you in have machines with all your supported browsers installed so you can launch your functional tests in those browsers. This works both locally or in CI tools like Travis.
disclaimer: I work for the company that builds and maintains FuncUnit and Testee - the tools are free and open source and this is not an attempt to promote our company.