yeah that might be a issue,
a invisiable hinge like this
http://www.woodcraft.com/Product/2001079/361/Hinge-Invisible-12-x-134.aspx ( 1st link I found) might be a option, but I don't care for them.
There are also face mount hings that are simlar to european hinges that would work, but they can be a little harder to
find wood tools and don't get the door "close"( about a 1/4") to the frame.
A box hinge is also another solution, but you will be able to see it from the side. You won't be able to see it from the front.
If you are not set on having doors that swing out, there are many other options.
There are littertly thousands of hinges out there, its just a matter of finding the right one. A cabinet shop supply house or a higher end wood working store should have/can get something that would work for you.