Check out this website Yamamoto Dendrobiums Hawaii They are located in Hawaii and have excellent info on care and hints for growing dendrobiums. Good luck!!!
Welcome to the Orchid Board. usually you leave the canes as they provide nutrition to the rest of the plant even without leaves or blooms. So, I would keep them there till either they are old and shriveled, or you have too many bare canes.
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"We must not look at goblin men,
We must not buy their fruits:
Who knows upon what soil they fed
Their hungry thirsty roots?"