I’m a veteran of this situation and have tried various techniques. What they mean is don’t completely submerge the toy or put it in the washer. The main problem is soaking the stuffing, which can get clumpy or damaging unwashable parts (e.g. suede collars, etc.) Other than that you get get it pretty wet. Try sponging on shampoo or Woolite, and then rinsing the same way.
I have resorted to putting favorite toys in the washer and dryer, with some fluffy towels for cushioning, if they got thrown up on or something. They usually come out okay, although the fur is never quite the same.