I had this issue. You can do what home builders do when they pour concrete driveways. They "sleeve" under the slab of concrete. You however will have to do it after the fact. Go to a home improvement store and buy a 3-4 inch PVC pipe and caps (no PVC glue). Dig down on both sides of the walkway about 6-8 inches and saturate the dirt with water. Cap both ends of the PVC pipe and use a rubber mallet to pound the PVC pipe under the walkway. Remove the caps. At the end you will be able to simply push any drip line through the open PVC pipe and route it where you need.
Hope this helps.