If you are seeking to place the web browser directly in the front panel, then just use an ActiveX container control with the Web Browser ActiveX object in it. If you wish the browser to be spawned externally, then I believe that your system exec approach should work. Did you have problems using that?
Also, if you are opening a web browser to view images being captured by a webcam device, then a better solution may be to use the webcam directly from within LabVIEW. A decent LabVIEW webcam library can be found at
www.mindofpete.org in the ideas section.
Pete