Decomposition of the body in the earth (after burial) is the slow oxidation of the body tissues. Cremation, on the other hand, provides rapid oxidation.
No casket is legally required for cremation, just a simple container, which is strong enough to hold the body. This could be a box of rough boards, pressboard, or heavy cardboard.
Some crematories accept metal caskets; most require the container to be combustible.
Some jurisdictions have laws prohibiting the scattering of remains; others require a permit. Ask your funeral director.
Also, ask if there are any firms in your area that specialize in unique ways of distributing the remains, such as a plane to spread them over a mountain, or a ship to scatter them at sea.
Think of places that were especially loved by the deceased, close to home or far away. You can walk in the woods, by a favorite lake, or on the old family farm.
Be sure to ask permission if you want to use private property.
What about using the remains to create new life, by planting a tree? Some survivors choose to mix the remains with the soil in flower beds and rose gardens at home. Every time the roses bloom, you will be reminded of your loved one.
If you decide to do this, however, consider what will happen if, some day, you move away.