That 2nd wiring diagram will work, but there are points to note.
The ‘stereo jack’ refers to the barrel-type jack supplied with the Ibanez-style kit the diagram was drawn for. Whilst you can get mono (TS) barrel jacks from Switchcraft, the Chinese kits have standardised on using a ‘stereo’ (TRS) style barrel jack. The term ‘stereo’ is misleading, as they are rarely used for stereo outputs on guitars and basses, but the third terminal is more often used to switch battery power on active circuits (most common on basses). So despite being a TRS jack socket, only the T and S contacts are used, so just wire it up to a standard output jack as normal.
The 2nd wiring diagram has the volume pots wired up differently to the 1st. The pickup signal now goes to the central wiper connection, with the output from the end tab on the pot (reversed from diagram 1). This is to prevent the output from one pickup being grounded when the other one is set to 0 i.e. the same as selecting a single pickup on the switched version. But this means that both pots are always connected to the pickups, halving the resistance the pickups see to ground.
In the switched version, when selecting just the neck or bridge pickup, they’d gave 500k resistance to ground at full volume, but with the 2nd arrangement, having one pickup on 10 and the other on 0, the pickup on 10 would see a 250k resistance to ground across the volume pots. This will knock off some of the treble and move the pickup’s resonant peak frequency down a bit. So the single pickup sound of arrangement 2 will sound a bit duller compared to arrangement 1.
It’s a bass, so this may not be a problem for you, especially if the pickups are quite bright sounding to start with. The both pickups on situation will sound just the same though.
But if you like to have a bright sound available (its easy to loose treble but harder to add it) then you can always use 1Meg volume pots instead, which will give the original 500k resistance to ground through the pots. This will mean that the ‘both pickups on 10’ sound will be slightly brighter than before. Keep the tone pots at 500k.
Swapping the volume pots is something you can do at any time, so you can see how it goes with the original values and see what you think.
If you want brighter sounds, you can always fit some mini toggle switches so you can have the pickups in series, parallel and split modes. If you don’t want two mini-toggles you can have a common tone control and fit a single 3-position rotary switch for common pickup mode selection, which still gives lots of sound variations.