What caps do I need?

I don't have the partlist for the WSX. But why recap? Does the machine not work anymore, or do you just want to recap for the sake of it?

The machine is 35 years old. A recap is generally a good idea with a machine of that age.

Yeah well that's my point. If it aint broke, don't fix it is my point of view. Of course, batteries should be replaced if they are of the leaky type. But those pcb's are all 35 years old as well, and for example the pcb of my ColecoVision and Philips 8250 are both rather brittle, and at some point the top layer is 'bubbling' up. Removing components should be done extremely careful in order not to do damage like ripping of a trace.

Now that's different for other machines, for example my Amigas have very well built pcb's.

But anyway, replacing working components, I personally don't see the use in that. If they worked for 35 years, quality is pretty good after all :-)

Show us the result anyway

Electorlite caps don't last forever indeed, but it would surprise you how many of them still have the desired capacity and still low esr, as if they were new. Visual inspection is important to not be fooled by them.

If you take a bit of care, you won't destroy your mainboard. Just don't use too much heat, not too low either because then you take too long, and absolutely do not stress the pads. Luckily the used solder was still leaded back in the day.
Don't be shy with flux and always have some fresh solder on the iron to instantly liquify the solder on the board. Cleaning the holes is easiest with a desoldering gun or with a high resolution wick (not just some loose copperwire).
If you do happen to waste a pad, that's not the end of the world. The trace can be scraped a bit. Everything can be fixed. Just don't let it get that far.

I've not recapped my Panasonic MSX2+es, only replaced the PSU and upgraded the RAM to 512KB. I did not run into issues with the pads, so they should be safe enough. The only cap I've seen being replaced is the big one in the PSU, due to some unstable video output.

I'm not sure if there's already a list of dangerous suicidal MSXes, but any with a HIC board in it has dangerous caps on them (the last Sony MSXes and some Panasonic MSX2s). Don't wait, fix now. When it comes to batteries, the only machine I've encountered is the Philips NMS8245. Cut that battery out now if you love that machine. They will leak just as certain as the caps on the HIC boards. Other machines I've seen don't have suspect batteries. They just lose their capacity, so replacing them is still useful if you value the RTC's functions.

Replying the original question, I found this list for its brother, the FS-A1WX. Probably the FS-A1WSX has a nearly identical list.

That said, I second the opinion that the Panasonic 2+/TR models very rarely need a recap, since they have excellent quality Rubycon capacitors.

OTOH, the MSX1 and MSX2 models by National/Matsushita have Matsushita capacitors. Back then, those were very mediocre quality capacitors.