Indeed. The documentation said Alt-Space for Unix and Alt-Shift-Space for Windows which are both wrong. For both systems the default is Ctrl-Shift-Space. I updated the docs, thanks for reporting.
Glad I could help :-)
It seems this isn't possible. At least the Scintilla documentation (the calltip window with the arrows is drawn by Scintilla, Geany only requests it and fill it with data) only talks about clicking the arrows with the mouse, it seems it isn't possible to use the keyboard for that. Or I'm missing something.
I have taken a look at Scintilla docs and it seems you are right. God dammit!
But I assume, that you are depending on SCN_CALLTIPCLICK, to change the content of the calltip right? So you have to access somehow the calltip content. Can't you just assign some keys in Geany and call the same function? Or are you filling the content of the calltip first and only then everything is done by the Scintilla?