Cleaning nightguard while camping/backpacking

Does anyone have any tips for cleaning a nightguard while camping? I usually wash mine with clear soap everyday at home but I don't want to harm the environment with soap. I know not to use soap near a water source but is biodegradable soap safe for the environment away from a water source or should it be avoided all together?

Unfortunately I couldn't go without it even for a short trip so any tips are appreciated!