There is no reason why you could not exclude a particular credit from a consolidation managed by a debt counseling service. Tell the service provider that you wish to exclude the credit card and pay it directly for reasons of your own. Tell the service provider which credits you want included in the consolidation. Typically, participation in a consolidation plan provided by a debt counselor is voluntary. You can discontinue the plan at any time, or modify it to whatever extent you wish. If the debt counselor providing the service disagrees with your choices they may wish to terminate their services.
With credible debt counseling services there should be no fees and no binding contractual commitment. If they want to charge you a fee or ask you to sign a contract my advice would be to respectfully decline their services. If you’ve already signed a contract or paid a fee, you might want to find out how you can terminate the agreement. If they want to charge a penalty for doing so, contact a good, local lawyer. Sometimes just a letter from your attorney will convince them to extinguish the agreement.