Any oil with a solvent has the potential to be a fire hazard. Most experts recommend submerging the rag into a bucket of water with an airtight lid, but very few people actually do that. You should make sure the cloth is flat and can dry completely.
If you bunch the rag up after using it, escaping fumes turn up the heat and are in danger of combusting. You may find yourself walking into a fire hazard.
Oils should never puddle on your wood surface. Make sure you’ve correctly wiped the excess away before allowing it to dry.
Options that contain solvents will need more than just water to remove. You’ll need a paint thinner or other removal agent.