Cycle is not going to help much. you wont really be adding any good bacteria unless the produc is refrigirated from the start. its likely you bought that cycle from a shelf. i have used cycle in the past and it doesnt do anything good or quicker.
Its best to just be careful with your filter media, and only rinse it off in tank water. then keep it submerged in old tank water whuile youre doing all the cleaning. dont us soap or bleach or untreated tap water because youll kill all the bacteria in the filter media. after youve filled it back up with treated tap water, pop the old filter media back in and raise the temps to 80F. add a bit of stress coat. are you using that as the dechlorinator? if so be sure to treat the tap water outside of the tank to avoid exposing the bacteria inside the filter, filter media, and on the decorations to tap water.