The greatest risk is that unless you know the source of the stain, it can be very difficult to define the appropriate concoction to remove the stain.

Some of the stain removal chemical's vapors are strong enough to remove paint or the finish off wood in the area. 

Costs will vary depending on the number of treatments required, cost of materials, and area affected.  What is clear is that this is an area where with the appropriate guidance the stone owner can do themselves more cost effectively than having a craftsman perform this service.  You are better served to have a craftsman periodically seal your stone.