Amazing as I have several mice here and the all work 100% in both JFDuke3d and JFSW and I have always had my Next/Previous weapons on the wheel.
Try copying and pasting my Mouse controls into your Sw.cfg
[Controls]
MouseSensitivity = 42588
ControllerType = 1
MouseAiming = 0
MouseButton0 = "Fire"
MouseButtonClicked0 = ""
MouseButton1 = "Open"
MouseButtonClicked1 = ""
MouseButton2 = "Weapon_7"
MouseButtonClicked2 = ""
MouseButton3 = ""
MouseButtonClicked3 = ""
MouseButton4 = "Next_Weapon"
MouseButton5 = "Previous_Weapon"
MouseAnalogAxes0 = "analog_turning"
MouseAnalogAxes1 = "analog_moving"
MouseAnalogScale0 = 65536
MouseAnalogScale1 = 65536
MouseDigitalAxes0_0 = ""
MouseDigitalAxes0_1 = ""
MouseDigitalAxes1_0 = ""
MouseDigitalAxes1_1 = ""
JoystickButton0 = "Fire"
JoystickButtonClicked0 = ""
JoystickButton1 = "Strafe"
JoystickButtonClicked1 = "Inventory"
JoystickButton2 = "Run"
JoystickButtonClicked2 = "Jump"
JoystickButton3 = "Open"
JoystickButtonClicked3 = "Crouch"
JoystickButton4 = ""
JoystickButtonClicked4 = ""
JoystickButton5 = ""
JoystickButtonClicked5 = ""
JoystickButton6 = ""
JoystickButtonClicked6 = ""
JoystickButton7 = ""
JoystickButtonClicked7 = ""
JoystickAnalogAxes0 = ""
JoystickDigitalAxes0_0 = ""
JoystickDigitalAxes0_1 = ""
JoystickAnalogScale0 = 65536
JoystickAnalogDead0 = 1000
JoystickAnalogSaturate0 = 9500
JoystickAnalogAxes1 = "analog_moving"
JoystickDigitalAxes1_0 = ""
JoystickDigitalAxes1_1 = ""
JoystickAnalogScale1 = 65536
JoystickAnalogDead1 = 1000
JoystickAnalogSaturate1 = 9500
JoystickAnalogAxes2 = "analog_strafing"
JoystickDigitalAxes2_0 = ""
JoystickDigitalAxes2_1 = ""
JoystickAnalogScale2 = 65536
JoystickAnalogDead2 = 1000
JoystickAnalogSaturate2 = 9500
JoystickAnalogAxes3 = ""
JoystickDigitalAxes3_0 = "Run"
JoystickDigitalAxes3_1 = ""
JoystickAnalogScale3 = 65536
JoystickAnalogDead3 = 1000
JoystickAnalogSaturate3 = 9500
JoystickButton8 = ""
JoystickButtonClicked8 = ""
JoystickButton9 = ""
JoystickButtonClicked9 = ""
JoystickButton10 = ""
JoystickButtonClicked10 = ""
JoystickButton11 = ""
JoystickButtonClicked11 = ""
JoystickButton12 = ""
JoystickButtonClicked12 = ""
JoystickButton13 = ""
JoystickButtonClicked13 = ""
JoystickButton14 = ""
JoystickButtonClicked14 = ""
JoystickButton15 = ""
JoystickButtonClicked15 = ""
JoystickButton16 = ""
JoystickButtonClicked16 = ""
JoystickButton17 = ""
JoystickButtonClicked17 = ""
JoystickButton18 = ""
JoystickButtonClicked18 = ""
JoystickButton19 = ""
JoystickButtonClicked19 = ""
JoystickButton20 = ""
JoystickButtonClicked20 = ""
JoystickButton21 = ""
JoystickButtonClicked21 = ""
JoystickButton22 = ""
JoystickButtonClicked22 = ""
JoystickButton23 = ""
JoystickButtonClicked23 = ""
JoystickButton24 = ""
JoystickButtonClicked24 = ""
JoystickButton25 = ""
JoystickButtonClicked25 = ""
JoystickButton26 = ""
JoystickButtonClicked26 = ""
JoystickButton27 = ""
JoystickButtonClicked27 = ""
JoystickButton28 = ""
JoystickButtonClicked28 = ""
JoystickButton29 = ""
JoystickButtonClicked29 = ""
JoystickButton30 = ""
JoystickButtonClicked30 = ""
JoystickButton31 = ""
JoystickButtonClicked31 = ""
JoystickAnalogAxes4 = ""
JoystickDigitalAxes4_0 = ""
JoystickDigitalAxes4_1 = ""
JoystickAnalogScale4 = 65536
JoystickAnalogDead4 = 1000
JoystickAnalogSaturate4 = 9500
JoystickAnalogAxes5 = ""
JoystickDigitalAxes5_0 = ""
JoystickDigitalAxes5_1 = ""
JoystickAnalogScale5 = 65536
JoystickAnalogDead5 = 1000
JoystickAnalogSaturate5 = 9500