Default RJ45-> PS2 and RJ45-> SNES button mappings

What are the default mappings for an RJ45 adapter assuming these are the 8 buttons:

QP MP HP 3P
QK MK HK 3K

I would like the PS2 to be:

^ R1 L1
X O R2 L2

and SNES to be:

L X R -
Y B A -

I know there’s 2 standard fight stick stups. Mine’s the Nuby/Capcom standard. The other one is

L1 ^ R1
L2 X O R2

The Ascii standard.

Also someone suggests it might be in the game pad mode where for SNES is:

Y X L
B A R

If either standard is “wrong” and I don’t want to change the wiring from DE37 to the Toodles Cthulhu, what should I do to accommodate the standard I want.

The main reason is I want to play Super Mario World, Mega Man X, Castlevania IV, Contra IV, and Super Ghouls N Ghosts, all of which I don’t think have joystick adjustments and have are optimized for pads where the YBA bottom row would be better than the BAR bottom row.