Most of this has to do with running, but it’ll help with your walking shin splints also.
I think the first thing you’d want to try, and the easiest, is to go with minimal shoes, like I wear, so they don’t interfere with natural movement.
1. Learn to not be a heel striker when running. land midfoot to forefoot.
2. Therefore, wearing minimalist shoes or barefoot is best, as “running shoes” and anything with a heel or too much cushion enables an artificially wider gait, enabling you to heel strike = BAD.
Minimalist shoes makes natural movement possible and strengthens your arch, and the other foot muscles. (Think about it. An arch support is like a cast. What happens to your arm muscle after it’s been in a cast for a whole month? It atrophies. When your arch isn’t asked to do it’s job by supporting your body, it will atrophy. What a great gig DR Scholls has set up, he sells products that perpetuate the symptoms they claim to fix!)
3. Don’t over-stride. Land with your feet closer to underneath your hips, not with your feet landing ahead of your hips.
4. Don’t push off with the toes. Learn to move at the hips.
Look into pose running technique. (far right image)
Some quick fixes in this 6 minute video too. http://www.mobilitywod.com/2011/06/episode-270365-mobrx-for-shin-splints.html