(fitting perhaps, since your ship is carrying the dead)
Not quite carrying the dead exactly, the first crew just happened to die and be reduced to little piles of ash (which Starfleet believes they collected all of)
Okay, but you get the idea.
Anyways, did you have a registry number in mind? I'm curious because I had a few theories on what number range a ship commissioned in the 2260's would have:
Now we all know they were in the 1700's by 2245. They supposedly reached 2000 in 2284, and ships in the 1900 range were in service in 2278. (I figured out years ago that if the Bozeman was launched not to long before it disappeared, that would mean Starfleet was commissioning an average of about ten ships a year in the late 2270's/early 2280's).
I'd suggest registry in the mid 1800's.