First do NOT flip it on your hand, if you halve a nice moist cake it will almost definitly crack and break. And Yes you can do it with any shape. A really good way to keep it form stick and breaking in one corner is to do the folowing:
Using parchment paper or waxed paper, cut a "pattern" around your pan, but make sure it is approx 1/4-1/2 bigger than your pan.
Using shortening or cooking spray coat the bottom and side of your pan. Place the parchment paper inside the pan and press down along the edges. And grease the paper as well
Fill with batter and then bake. When you take it out of the oven let it cool on a wire rack for about 10 min, and run a knife along the edges. Now put the cooling rack on top of the cake in the pan. Flip the cake onto the cooling rack by turning upside down. Remove the pan you baked the cake in and then peel off the paper. Perfect everytime.
Also another hint for when you ice/frost the cake...wrap in plastic wrap and freeze overnight. Then frost, this will help to prevent it sticking to your icing and coming up in big chunks. Then when you are done frosting it let ot thaw and it will be great.
Okay one more thing, do you know about doing a "crumb layer" this is a thinner layer of frosting that just sticks any loose crumbs to the cake so they don't end up in your finished pruduct. Then put the pretty layer on topof the crumb layer and decorate.
Hope it turns out well.