Sure it's possible. I'm partial to Red Oxx but any carry-on sized non-wheel bag will do so long as it's not so cheap it falls apart on you.

You'll have to be more judicious in what you pack. Shoes are my big challenge—I've yet to find the right balance between style and quality. Right now I tend to wear Merrel hiking shoes in all black. They look like sneakers but I can walk all day long and never get tired. Not, however, very stylish.