With Fallout 4 VR, you could
bind console commands to keyboard keys, because Fallout 4 had this feature built in(left over) from the development process; This allowed triggering of many actions despite the mission keyboard functionality.
Skyrim(SE included) does not have such a feature, and despite the engine upgrades for Skyrim VR, it was not ported over either(I've tried setting it up in the config, but got no response to the keys).
There are hotkey binding mods for Skyrim(SE), however they depend on Script Extender, which will not be ported to the VR version according to its developers(this is the case for FO4 VR as well).
Additionally, Skyrim(SE) also lacks the "CGF" console command, which made it easy in FO4(VR) to run simple utility scripts(toggling the pipboy radio for example, as available with FO4 hotkeys).
Skyrim VR does respond to most normal keyboard binds from the regular game; Left and right mouse button attack with right or left hands, WASD moves the character, space jumps, J opens the journal, etc...
One thing you could have VoiceAttack do is press/hold the "Z" key for shouts, if you want to try "FUS-RO-DAH" irl
Just make sure the Skyrim VR window has focus, otherwise it won't detect the input.
I'd experiment more, but Skyrim VR is unplayable on my machine right now; Apparently I'm not the only one, but when any sort of menu is open(including the map), the CPU usage jumps to 100% and my entire computer freezes up every few seconds.
This also prevents any type of interpolation(ASW) working so I get stuck with a static image in the HMD, which makes me nauseous.