It is seems like you can use the class
Interaction and the function of "shell"
VB.NET DEMO CODE
Dim procID As Integer
procID = Shell("the path of your exe file", AppWinStyle.NormalFocus)
you can add the url after the string of you exe file with a blank for example:
..\iexplorer.exe www.facebook.com
the AppWinStyle is a enum type include such styles
AppWinStyle.Hide
AppWinStyle.NormalFocus
AppWinStyle.MinimizedFocus
AppWinStyle.MaximizedFocus
AppWinStyle.NormalNoFocus
AppWinStyle.MinimizedNoFocus
the return value is the process ID of exist exe file.