daisy *hates* not being able to feel something under her feet, so that would not be an option for us. however, if your doggie doesn't mind and isn't uncomfortable, then go for it.
i have a puchi bag for daisy that's a little too femme for my bf to tote her around in, but they have a lot of other styles to chose from such as messenger bags (
http://www.puchibag.com/type_mailbagcarrier.htm) and backpacks (
http://www.puchibag.com/type_backpack.htm)that can be perceived as being more masculine.
http://www.puchibag.com/index.html