I just got an Isolette III last week, and I ran into this problem. After tinkering with it a bit, there seem to be two solutions. . .
1. Don't wind your film until you're about to take a shot. (This is stated in the manual, by the way!) Even when loading the film, you can stop short of the first frame and slip the camera into your bag/pocket, then finish winding when you bring it out.
2. You can always trigger the shutter by tugging on the connector bar underneath the bellows. It pivots side-to-side, so you actually tug it lightly towards the side of the camera, and then it's almost as easy as using the normal release on the body.