I'm afraid there is no way to do it. Everything is stored in the System\rayne.ini file. It has gamecontrol entry, which can only have one value (from what I see it's 0 for mouse and keyboard and 1 for gamepad). There is also Controller_0_type entry - with values 0 for mouse and keyboard and 2 for gamepad (and probably 1 for joystick, but I can't verify it).
The interesting part is that there are entries for Controller_1_type, Controller_2_type and Controller_3_type, but I don't see a way to make them work at the same time.
The only thing that may help is Controller_0_pc_stick entry - you can try setting it's value to 1 if it isn't set already, but I'm afraid it won't help. It's still worth a try.
(And I don't have the GOG version, so this entry may not even be there).

You'd have to map the joystick buttons to keyboard keys...
Still - why would you want to do that ? I imagine you want to move with the joystick and aim with the mouse... Why not simply use a k+m combo instead ?

For analogue movement I guess. Neither using a keyboard nor binding joystick buttons / axes to keys will solve it.