COBRA is offered to each person on an individual basis, so yes, you can opt to take one person off the plan. If you're in reasonably good health, I'd lock in an individual health insurance plan before something changes that and you (or someone else covered) becomes uninsurable. Unless you live in NY/MA/NJ or other guaranteed-issue states, it will probably be less expensive than COBRA too.
Disclaimer - I am an independent insurance agent. If the above message contains insurance-related content, it is NOT intended as advice, and may not be accurate, applicable or sufficient depending on specific circumstances. Don't rely on it for any purpose. I do encourage you to consult an independent agent for insurance-related advice if you have a question that is specific in nature.