Nope -- unfortunately that's one of the limitations of PICO-8 supporting dual-stick.
If you're playing single player in the native app you can use P1's directions to move and P2's directions to shoot, but PICO-8 does not let you map different player's movements to the same controller. You can remap keyboard controls there, but most people have a pretty hard time playing dual stick on a keyboard (there's a lot more buttons and it can get overwhelming).