Though the contemporary English equivalent of the word is to shake, shoogle implies a gentler action; you wouldn't really shoogle a can of deoderant, nor would you shoogle someone awake if you needed them to be up urgently (though you can certainly shoogle someone to sleep).
What does Shoogle mean?
/ (ˈʃʊɡəl) dialect, mainly Scot / verb. to shake, sway, or rock back and forth.
What does the Scottish word Shoogle?
shoogle: shake, wobble, move from side to side.