Whatever feels good. We put a lot of folks into Brooks running shoes for walking. My all-time favorite walking "shoes" are my Chaco Z-1 sandals. I even ran in them (back when I was running).
You'll get evil shinsplints in any shoe that makes you crash onto the sole of your foot after heelstrike, because your dorsiflexors will be struggling to deccelerate your tibia. For some folks that could be running shoes. For most folks that'll be hiking boots. New Balance makes a shoe specifically for walking that reinforces the heelstrike-toeoff roll. That shoe makes my feet hurt.... And my Technica hiking boots don't cause me any trouble walking on pavement....
Walk in your runners if they feel good. If you're not happy with them I'd say go to a very good run/walk sports shoe store and try out lots of stuff. Make sure they watch you walk and look at the wear patterns on your old shoes.
At one point I had 3 pr of Brooks Addictions: one for running, one for walking, and one for wearing around.
Do what works!
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson