That is technically possible using the mouse move action, though I'm not sure how viable that'd be, especially in combat
You may want to look into enabling or turning up aim assist, perhaps through a mod, if that is possible for Skyrim.
To have the cursor/view move continuously, similar to the WASD keys being held down, you'd want to use a(n infinite) loop (which is an advanced set of actions)
You could then use a command (ideally separate from the "stop" command for movement, so you can keep running when necessary) to stop your mouse movement commands, as well as having directional commands stop the command for the opposite direction, E.G. the "left" command would stop the "right" command, as vice-versa
It may be more practical to rename the WASD commands to something like "forward" "backward" "star" "stall" (the latter two seem less awkward than "strafe right" and "strafe left"), so you can use "up" "down" "left" "right" for mouse movement. To stop mouse movement, perhaps "halt"