Bricks, Masonry, Asphalt and Concrete - Pebble stone walkway..can I add Concrete?

I have a 50' walkway made out of slate and pebble stone. The stones are just used as filler between the slates..The stones make such a mess especially in the winter time when I need to shovel. Ideally we would like to do brick but that's really expensive. Is there any products I could use...concrete, etc do mix with the pebble stones to keep them in place? When we built the walkway we dug down about 8 inches and have about 6 inches of blue stone dust...if I removed the rocks and just left the blue stone would that get tracked into the house? I would appreciate any suggestions of how to keep the stones in place or other materials to use between the slates instead of rocks.