Wouldn’t a non-hyperspectral spaceship be much more remarkable than a hyperspectral one?
Most materials aren’t terribly ideal black bodies; but even the ones that are significantly reflective at some wavelengths, or are worth pointing a spectrometer at, tend to have a lot going on(even if it’s at an order of magnitude lower intensity than the visible spikes) from very, very, deep IR up to at least the middle of the visible range; potentially higher if warm, under stimulated emission, or reflecting light from a star or other source that is very warm indeed.
If there’s something that would give an object very, very, strong not-in-kansas-anymore vibes it would be picking something up that is perfectly monochromatic down to the limits of your instruments; or emitting at a few specific frequencies with more or less perfect bandgaps between them.
Even nominally-monochromatic light sources like lasers tend to exhibit some non-ideal frequency slop around the edges(though it falls off pretty rapidly outside of garbage tier diode lasers); and things whose natural habitat isn’t ‘bolted to a vibration dampened table in a photonics lab’ tend to emit fairly promiscuously all over the spectrum.