Yes! You can do yoga without doing a specific pose, such as down dog. One of the things I love to show people is how to modify a class to fit their individual needs. When my husband was working in Alaska, I customized a live stream video class for a group of his coworkers without down dog because of their previous shoulder injuries. I gave them alternatives of doing cat and cow pose on their hands and knees instead of doing a more traditional plank / down dog flow. They were still able to do a flowing yoga class, while limiting the weight and stress on the shoulder joints. In addition, they were able to take those modifications confidently into any other yoga class in their future practice.
Have you done a no down dog class before?
How can I help you customize your yoga practice?
Let me know in the comments!