To me I find that the single coil pickups of the jazz bass always impart too much of a "nasal" midrange characteristic, especially in the upper mids, to be able to pass for a Wal sound.
I'm sure that with the right preamp and playing technique you could probably do a pretty decent take on Mick's sound, but if you're really serious about getting it, you'll need to spend some money.
The common way to replicate the Wal tone is often said to be:
1) Get some custom pickups with the coils and wiring made to replicate Wal pickups. If this is impossible, find some big humbuckers with a naturally dark sound. IMO, Bartolini do this well.
2) Get a custom preamp from ACG with the low pass filters.
3) Put them in a bass with a mahogany body and and ebony fretboard.