Is there a window or portable AC system I can use with an awning window?
Window unit air conditioners rely less on the ledge and more on the window itself to keep from falling.  The unit is surrounded by a frame.  You carefully set the unit in the window with the frame tilted forward some towards you.  You then lower the window until the A/C frame can rest on the frame of the window itself.

Portable air conditioners usually (as I understand it) have an exhaust hose that you use to vent the hot air outside.   You could put this hose out the window - but you'll want to make sure the rest of the opening is blocked off so as to not allow outside air back in while you're pumping out the hot air.