You'll have better odds in getting the best weapons if you make some time before before going back to get your order.
Go out, look around, enter some houses, talk to people, peek their personal stuff.
If you just leave>enter, I'll mostly get the shitty weapons.
BUT
If you were refering to weapon types, (ie: sword, blade, rapier), it's simple: the smithy will make the same weapon type as the one you have equipped when you order it. Only exception are accessories and cursed weapons.
Also, you don't need to shut down the Saturn and re-swap. A single A+B+C+START (don't tell me you didn't know this magical button combo?) will take you back to the title screen. Works for 99% of the games.