Just found an older site listing "the future waves" of Johnny Lightning Star Trek ships... it messed up the composition of the waves but mentions
Copernicus Shuttlecraft with atmospheric reentry damage
Could be this one from (the astounding awful) ST:5
or this one from the animated series (unlikely):
or this one from the 1701-D:
I guess you could (unsuccessfully) argue that the original 1701 had an unseen regular Class-F shuttlecraft Copernicus too... do you think JL would just repaint the existing Galileo... it seems unimaginable (but extremely likely).
I wouldn't mind any of them except the repainted Galileo.
It seems the mystery is over, though...