All katanas can be used in Draw Out, excluding the following situations:
1. A particular katana has not yet been acquired
2. All katanas of one type (Chirijiraden, for example) have been equipped to the party, and there are thus none of that type in the inventory
3. The necessary JP for a Draw Out ability has not yet been amassed/applied
None of the Proposition Treasure swords is a katana (including the Magi-Sword), and neither are any of the ninja swords, so I'm going to assume that situation (3.) is what you were looking for.
