I don't think there is a software way, if the app you linked to can't remap the scroll wheel. The quick way is to wire the spinner to Z axis, but how depends on which spinner you have and how it's connected to the computer. The next step is to add a 2 way 2 pole switch so you can swap from Z to X axis and back.
Somethings you didn't touch on are which spinner you have, what other games & apps you're planning on using. Mame? While mame can remap so the dial type input reads from the Z mouse axis (aka scroll wheel), the scroll wheel normal step is 40 unlike the X & Y's one, so you need to set mame sensitivity to 1/40 of what you'd use for the X & Y axes. If you have a high res spinner (TT2, TT-HL, SpinTrak), though, most likely the values are too high. And most games don't support multiple mice like mame, let alone remapping the individual axes. All these are why I mentioned the hardware switch.