I have the wiring diagram for the 1993 through 1997 Altima and it's typical of what I remember. It uses one flasher module. I've never seen a car (except pre-1970 retrofits) with two different flasher modules, but that doesn't mean they don't exist, it means I haven't seen one.
Some cars may still have a place you can get 12 switched from the hazard switch. These 93-97 Altimas do not.
You would need a diagram of your car to be sure, or as MikeMI suggested as an alternative, use a retriggerable one shot.
If your LEDs don't consume much power, you could run them from the blinkers. Charge a 470 uF 25V capacitor thru a diode from each blinker and power the LED from the capacitor. If it almost works, try a larger capacitor.