Hi & welcome Beth,
For most orchids its best to wait to repot until after the plant blooms unless it is declining quickly. Some orchids can be shocked when transplanted in bud/bloom and drop their flowers.
Do not prune off the old canes. The old canes store water and food for the growing plant and the blooms usually come from year old canes. Occasionally older canes can also rebloom. The only canes you should ever remove are brown and mushy canes or ones that are completely dried up. Nobile dendrobiums are known to defoliate in winter and require a rest period which also includes withholding fertilizer. Their new growth generally starts in spring.
Itís good you put drain holes in for the orchids or it would have had a slow death. When itís finished blooming I would remove it from its current container and check the roots. If any roots are dead or all mushy, remove them. Live roots are white or possibly light yellowish. You can tell the dead roots by the long thin strings which remain from the inside from when it was a healthy root. Nobile den's like to be potbound and you should put it in a container which can accommodate the current roots system (not too much room). A pot clip or bamboo stake can help you secure it if itís a bit wobbly. You could even get an orchid pot (clay pots with slits on the side) to help promote air movement through the potting medium.
Also, you need to check and see what your potting medium is. In my experience most dendrobiumís I have like a tree fern fiber mix which usually contains some sort of bark, perlite, and tree fern fibers. This allows plenty of air movement for the root system. Other mixes will also work, but this is just an option for you. Make sure itís not planted in dirt or soil of any kind; itís too heavy and doesnít allow the roots to breathe.
If you have the orchid inside make sure it has a bright window but no direct afternoon sun that could burn it. Direct morning sun is generally okay. Once this orchid is repotted you can start it on a fertilizer schedule. The trick with orchids is to apply a weak solution weekly. So whatever your orchid fertilizer says you want to apply at least half that (or less). I personally mist my fertilizer on once a week early in the day and on the 4th week of the month I just use straight up water to flush out any buildup.
Lastly, to increase humidity, if you have your orchid indoors, you can add a tray of pebbles w/ water underneath your plant. Just make sure the water level is below the pebbles and the orchid isn't sitting directly in the water. This helps create some humidity for the plant.
Hope I answered some of your questions. Feel free to ask me anything regarding my post.