jkhom,
There should be no need to cut the old canes unless you see any signs of infection that could risk the entire plant.
The old canes on my plant just shrivel and slowly fade completely.

I follow the usual "nobile" dendrobium culture for me Den. unicum. Heavy watering and regular feeding from April-September when the canes/leaves are in active growth and then switch to just occational misting in October. Then absolutely no water from November up to March (or until new canes start to grow).

The "No watering" part makes some gardeners nervous and it is tempting to give the plant some water. But these plants seem to really like that dry period in the winter time.