Ash Soan shares a playing technique for adding swing to shakers and tambourines by leveraging the natural physics of the instruments.
For shakers, instead of forcing a swing feel, Soan suggests playing straight 16th or 8th notes while adjusting your forearm position to control the swing. When the forearm is up, the shaker moves horizontally, resulting in no swing. By lowering the forearm so the shaker moves more vertically, gravity naturally introduces a swing. Any position in between allows you to find a sweet spot that is neither fully swung nor completely straight.
This approach also applies to tambourines, where playing it left to right results in no swing, while moving it up and down allows gravity to create a full swing.