If you want to sell fast without doing quiet title, the safest approach is to fully disclose that title has not been quieted, that title insurance may not currently be available, and that the buyer is taking the property subject to that risk. That usually means marketing it to cash investors, not retail buyers.
As for the deed, many sellers use a quit claim deed for that kind of sale, or in some cases a special warranty deed with very careful language and clear exceptions, but the key point is full written disclosure, not trying to make the title sound cleaner than it is. You can say it plainly: "No quiet title has been completed, buyer should do their own title review, and seller is pricing the property accordingly."