Your choice of browser should have nothing to do with your security software (unless you've somehow configured that software with some ludicrously over-cautious settings).
I use Firefox as my main browser but I occasionally launch Internet Explorer (without needing to close Firefox) in order to answer a question about the way that it works. Similarly, a few minutes ago I launched Chrome (in order to answer a question about it), while still leaving Firefox running. It would never even occur to me to have to make any changes to my security software in order to switch browsers. (Also, an internet café which I often use has IE, Firefox and Chrome on every machine, with different users preferring different browsers. The security software certainly doesn't need altering every time a new user walks in!)
You can have dozens of different browsers on your laptop (with them all running simultaneously, if you like). Your security software shouldn't need any alterations whatsoever (except, possibly, to allow for those browsers to receive automatic updates).
Chris