Cycling a tank with a living fish should never be done. You can cycle an aquarium without issue by tossing in a table shrimp or ghost feeding without harming a fish. Either method will cause an ammonia spike and get the cycle started.
On the damsel in a tank of that size, it's best to leave damsels to the larger tanks. I'd suggest at least a 50 gallon tank to give othe fish enough space to be with it.