It is OK to do cardio the day after a leg workout as long as you don't exceed your recovery capability. The signs of that are consistant pain or soreness and lack of increases or even decreasing strength, week after week. As an alternative to "all leg" cardio like running, stairmaster, bicycle, etc. you might want to try soem type of cardio that shares the work with the upper body like cross country ski, or rowing.
The best way to avoid shin splints is to stretch and strengthen your calves and shin muscles. I found doing slow, full range of motion calf raises, along with twice daily stretching sessions helped reduce my shin splints a lot.
