Yeah, so far so good but I need to drive it more to really consider this issue fixed.
I took some photos of the whole process, mostly because I thought I would need them later to put everything back together, but it was so easy it wasn't needed. Still, maybe this will help someone in the future, especially if you don't know where the screws and clips are so you don't break any hard-to-find dash panel:
First thing you need to do is take off the kick panel. It's held in place with one screw and a couple of clips. The clip shown here is very, very strong. You can see the other one in the next photo. You may have to remove the plastic door sill first. It's clipped on and just pulls up.
The reason for removing that kick panel is that there's a screw holding the bottom dash cover just behind it, here (also, the other clip for the kick panel):
There is another screw for the bottom dash cover on the other side, under the cabin temp sensor. Once you remove both, the panel slides towards the back of the car (don't pull down). Be careful as there will be plugs for the dimmer switch, temp sensor and electric mirrors still connected. You need to unclip all those:
Once the lower dash cover is out, you will be able to remove the steering wheel cover. First thing you need to take out is this plastic ring highlighted in red. It's held in by friction and just pulls out, no clips and no screws. Just use something sharp:
Finally, you need to remove the 5 screws at the bottom of the steering column cover. Once those are removed, be careful as the two halves of the cover are still clipped on. You can press on the sides of the upper plastic part to help release the clips. It's also easier if you loosen the steering wheel adjustment lever, gives you more room:
With the cover away, you will have access to the ignition switch. Two small phillips screws hold it in place. Unclip the connector, remove the screws and put the new switch in the same position.
Before putting everything back together, reconnect the new switch and test it.