The phrase "graceful way" means doing something with elegance, poise, and dignity. It suggests doing or handling things in a smooth and pleasant manner. Full definition
However, my point is that asking for referrals is a common business practice, so get over your discomfort and find graceful ways to ask. (slaw.ca)
Too gentle and leisurely to survive as a solid classic, though there's pleasure to be found in the cast's graceful way with comedy and their smooth ensemble playing. (rottentomatoes.com)
You can ask for referrals before, during, and after the sale, so I've included graceful ways to approach the topic at each stage of the transaction. (realtormag.realtor.org)