As stated in many stickies not possible on any firmware above 9.2 with or without flashcard. Don't update and hope a way is found. Updating only lowers your possibilities.
No, you can't downgrade on 9.3+ with or without any flash cart. If you have a NAND backup of a firmware that's 9.2 or older from this same 3DS, you need to get a hardware NAND mod installed. There's no other way right now to downgrade from 9.3+.