A wild guess, but it could be your shoes don't have much support inside, like arch support. You say the pain is on the outside of your foot, maybe adding some support inside your shoe help distribute the weight more evenly/comfortably.
It could also be that your new shoes have a different amount of varus/valgus built in. If your new shoes have more varus, it could be putting more pressure on the outside I think, so you could use a valcus insert to cancel out the varus built into the shoe. (Varus/valgus is an interesting topic you can read more about in a lot of places online). Some cycling shoes have varus built in, but a minority of people don't need that and are better off adding an insole wedge to cancel out the varus.
Remember cycling shoe comfort doesn't equate to walking comfort. I found that to be comfortable cycling, the arch is high enough that it's mildly uncomfortable while walking. Not painful, but definitely a higher arch than what's in my regular shoes. FWIW, that equaled the red Specialized BG inserts in my cycling shoes, but that's for me and I have pretty flat feet. I also have Specialized shoes that have 1deg varus built-in, and that's comfortable for me.
One interesting item: I haven't used these personally, but I've seen them recommended in many places online and they seem like a good idea: http://www.esoles.com/products/efit_supportive.aspx
They have modular/adjustable arch support so you can dial in what you need without having to buy several different inserts, it's like getting several different insoles but only having to buy 1. Or some Specialized dealers have a foot measurement thing to help you pick the right insole for your feet. The Specialized footbeds also come with varus/valgus wedges to adjust the angle of your foot, which may be something you need.
Experiment, you'll find things that work for you. Change one thing at a time, and make note of everything you change, so that you can undo your changes and dial in the things that work for you.