I just bought the same pedals for my commuter. They work with cleats or as a platform pedal. Gives you lots of flexibility to wear normal shoes or shoes with recessed cleats. For that reason alone I would say keep the pedals, buy new shoes. Here's the shoes I bought: http://www.rei.com/product/765129 . Very comfortable. Good enough to wear all day. I can't feel the cleats unless I'm on concrete floor or pavement.

Just for the record, I have the pedals and shoes with external cleats on my other bike. I prefer to ride with those, but walking in them sucks.