Mounting something to stud-less plaster exterior wall
There are probably king/jack studs on each side of the window plus a sill and a header. Your magnetic stud finder might not be strong enough to go through the plaster. They're good for finding drywall screws covered by joint compound but that's about it. So you either buy a more expensive stud finder or start drilling really small holes hoping to find the studs.  

Will the cabinet only be supported by the screws into the wall or will it also have legs? You can always use toggle bolts through the cabinet and through your wall.