Dendrobium Nobile branching?
 

Obviously I’m new to Dendrobiums. I have a Nobile (For the Kids) That has finished blooming. The old canes are all now developing branches like a tree might. I thought they might be keikis but I don’t see any roots forming. The plant is doing really well with the newest cane thicker and taller then the previous years. She bloomed really well this year so I’m puzzled. In all the pictures I’ve seen of canes, I’ve never seen branches.

Those are keikis. Sometimes the roots don't form until the shoot gets pretty big. They'll come along eventually.

Should I remove them or leave them?

If you're wanting new plants, you can leave them until they have roots and then separate them and pot them, but if you're not interested in doing that, it may be better to remove them so the plant's energy is focused on the main new growths.

Is it better to just snap them off or to use a sterile razor to slice them off. Thanks so much for the info/guidance.

It probably doesn't matter. If they're still young and tender, they may snap off easily. If not, you can cut them, but the result is the same either way.

If you care for the plant normally and get water on the keikii roots when they form, they shouldn't set the plant back at all. Plus you will have plants to trade. Wait to separate them until the roots are about 2" / 5cm long.