Fedora, rather your desktop environment, cannot control whether skype starts minimized. If skype has the option you can use it to start it in minimized mode where it's only a notification icon.
From what I see, there isn't a command line option, may be something in the GUI?
[ankur@dhcppc1 ~]$ skype --help
Skype 4.1.0.20
Usage: skype [options]
Options:
--dbpath=<path> Specify an alternative path to store Skype data files.
Default: ~/.Skype
--resources=<path> Specify a path where Skype can find its resource files.
Default: /usr/share/skype
--secondary Start a secondary instance of Skype.
--disable-api Disable Skype Public API.
--callto <nick>
skype:<nick>?<action>
These commands allow Skype links handling.
--pipelogin Command line login. "echo username password | skype --pipelogin"
--version Display version information and exit.
[ankur@dhcppc1 ~]$