Here's one suggestion: Get a big ziplock bag and fill it with water, and put the unused cigarettes in it, then throw it away to prevent fire.
Most post-consumer waste disposal is the responsibility of the consumer. Carelessly discarded cigarette butts are a frequent cause of fires. You should dispose of cigarette butts in the dedicated receptacles ONLY.
You can also take Recycle Nation's advice on how to recycle cigarette ashes and waste:
Your best option for recycling cigarette ashes and waste is a company called TerraCycle, which specializes in difficult-to-recycle waste. For several years now, it has operated a program to recycle cigarette butts, ashes and other waste products. To participate in TerraCycle’s Cigarette Waste Brigade, you first have to sign up for the program on its website. Save your cigarette waste in your regular ash tray or other receptacle. Over time (and once your cigarettes are fully extinguished), you can transfer that waste to a plastic bag or other container described on its website. Once you have collected a large quantity, place the bag in a box, print a shipping label from TerraCycle’s website and send your old cigarette ashes and waste away. TerraCycle takes your trash and turns it into pallets and other useful products. It also composts any leftover tobacco that arrives in packages. TerraCycle’s website explicitly states that it can accept cigarette butts, ashes, filters, rolling papers, packages of loose tobacco, the plastic that goes around your cigarette pack and the foil found within the pack. The only thing TerraCycle does not take is cigarette packages and cartons.
According to this paper: Regulating the Disposal of Cigarette Butts as Toxic Hazardous Waste by Richard L Barnes, Center for Tobacco Control Research and Education, University of California, San Francisco:
More than 5 trillion cigarettes are smoked worldwide each year, and all of them are disposed of in some manner. There are literally millions of points of deposit on the planet. They are dropped on the ground, tossed in trash bins and carted off to landfills with little or no thought being given by the smoker or society at large as to what that means to the environment. Regardless of how the butts are disposed of today, each one of them may pose a toxic hazard to the environment.
About 99% of the manufactured cigarette market is filtered cigarettes; filters degrade very slowly and thus become an accumulating mass of potentially toxic waste. Toxic substances are leached from the filter and tobacco residue that pollute waterways, and probably pollute ground water near landfills that are not properly constructed to contain such leachates. Aquatic life may be harmed by the toxic leachates, and the butts may cause physical harm when ingested by animals. Butts collect in municipal storm drains and then may empty into waterways, and can clog storm drains and sanitary sewer systems.
Get more disposal of cigarettes tips at Everettwa.gov.