While editing a path, how do I switch the current selection between  corner, smooth, symmetric auto smooth, using the keyboard ?

Obviously other than clicking on the icon ?

I can´t find any entries in the Preferences->Interface->Keyboard that do what you want - but you can zap through the 4 types of nodes by holding "Shift-key" down and clicking on a node.

Are you sure ? Can you specify you Inkscape version and OS ? 

Here on Inkscape 1.1.2, on Linux, this has no effect.

It just toggles the selection, as indicated in the status bar.

I´m on macOS; can´t tell about other OSs but the Status Bar is clear:

The keys and mouse reference is found in the help menu.

Node tool - Change node type.
 

Here is a data point.

I upgraded to 1.3.2 and I got this working with the Control  (not Shift ) key under Linux,

This allows to cycle between the mentionned modes.

Thanks.

So here you go:

Thank you

It's missing from the Tool Tip though.

Is it be possible to reassign the shorcuts ? Even if if means recompiling Inkscape, I don't care.

I don't have any use for C,S,Y,A and the required Shift is really annoying. I'm using Inkscape almost only to edit Bezier curves, and it would be nice if those shortcuts were easier to type.