MacOS – Launch apps full screen

Make sure you have "Allow Exposé, Dashboard and others to use the screen" in keynote preferences under Slideshow.

Then, before you slide over to Safari, press the "F" key to pause the slideshow. This prevents the slideshow from disappearing.

You can then slide over, or use Mission Control, etc without affecting the slideshow.

There is a bug here, to go back to the slideshow you have to slide back to it or click on the desktop in Mission Control; you can't click the Dock icon or Cmd-Tab back to it.
(Clicking the dock icon / cmd-tabbing will just hide the dock and menubar but not take you back to the presentation)

Also: When you get back to the slideshow, the first key press or mouse click unpauses the presentation, so you will have to click / press again to advance to the next slide.

Side note: instead of having keynote and Safari on separate desktops, you can have them both as fullscreen apps. This hides the Dock and Menubar, so when you show the web page, there is more room for it.

Just going into the main Mission control window will solve this, it will give a nice summary like view of all your open (fullscreen) windows. Another way to switch between fullscreen windows is selecting the "Window" menu item or the Safari icon in your dock and choosing the right window from there.

Edit

If you want to use a keyboard shortcut to accomplish this you can use an application that binds a keyboard shortcut to an Apple script, like FastScripts. The next step is placing the script in your /Library/Scripts folder and adding a shortcut to the script in the FastScripts preferences.

I'm not really good with Apple scripts, but this is a sort of working script that I made:

tell application "Safari"
activate
end tell

tell application "System Events"
    tell process "Safari"
        tell menu bar 1
            tell menu bar item "Venster"
                tell menu "Venster"
                    click menu item 14
                end tell
            end tell
        end tell
    end tell
end tell

The big problem with this script is this: The line click menu item 14 will make the first window that you see when you click on the "Window" menu item active, and changing it to click menu item 15 will make the second window active. However, obviously, this isn't included in my code, and I don't have the time to work on it today, so you can either ask someone else how to do this or wait until tomorrow.