Impossible. The Action Replay DSi is a cheat cartridge—it does not store game ROMs or saves. It patches game code in RAM. When you delete a DSiWare game from System Settings, it's erased from the DSi's NAND (or SD card if moved). The Action Replay has zero access to that storage.
Keep backups of your NAND/SD if you mod. Official DSiWare is permanently delisted. No recovery path exists through Action Replay or Nintendo support.