Upload & Sell: On
Since they are selling for around $600, it is still viable to repair, if a shutter is all you need.
If you are replacing, why not buy a full frame instead of the 1D4, since you have full frame lenses? A used 1Ds2 is especially attractive, as is the 1Ds3 with even better IQ and features. These should work for sports, and definitely for outdoors.