Hi Norm,
There is a koi in our ornamental pond that is missing the left front pectoral fin, has been missing it since it was a young fish, though there is the stump that moves as if a fin were attached. This fish thrives and swims normally. Also, there was another koi in a 55 gallon tank in the building where I work that regenerated the lower lobe of its tail fin which was bitten off by an aggressive fish. It, too, swam normally albeit with a slight limp, until the fin grew back. However, the more aggressive fish, after a year of bullying, finally finished it off.
Joe