The answer to this question resolves itself into two parts. First, whether a spaceship exiting hyperspace will be a source of gravitational waves. Second, whether gravitational wave detectors can detect these gravitational waves.
Any object with mass that accelerates (which in science means changes
position at a variable rate, and includes spinning and orbiting
objects) produces gravitational waves, including humans and cars and
airplanes etc. But the gravitational waves made by us here on Earth
are much too small to detect. In fact, it isn’t even remotely possible
to build a machine that can spin an object fast enough to produce a
detectible gravitational wave – even the world’s strongest materials
would fly apart at the rotation speeds such a machine would require.
Since we can’t generate detectable gravitational waves on Earth, the
only way to study them is to look to the places in the Universe where
they are generated by nature. The Universe is filled with incredibly
massive objects that undergo rapid accelerations (things like black
holes, neutron stars, and stars at the ends of their lives).
For a spaceship to be a source of gravitational waves as it exits hyperspace this spaceship must physically act as if it is an object with mass undergoing an acceleration. Effectively, the spaceship might be apparently decelerating, but this is still an acceleration.
Presumably the rate of acceleration will be determined by the time it takes the spaceship to exit hyperspace. The shorter the exit time, the higher the acceleration will be. Also, the more massive the spaceship is, the stronger its signature as a gravitational wave will be.
The strength of a gravitational wave signature is the more detectable it will be. Now existing LIGO systems can detect black holes merging, binary neutron stars, and supernovae. Therefore, the parameters that need to be manipulated to ensure the probability of a spaceship exiting hyperspace are its mass, the time to exit hyperspace, its proximity to the detector systems, and the sensitivity of gravitational wave detectors.
Since the OP wants the spaceship to be detected only by its gravitational waves, this sets an upper bound to the mass of the spaceship. For example, a Jupiter-mass spacecraft exiting hyperspace in a fraction of an attosecond might be the source of gravitational waves of sufficient strength to be detected. However, if a Jupiter-mass object arrived near Earth it would be readily detected because it would change the orbits of Earth and the Moon plus the satellites orbiting the Earth. Also, it likely to be big enough to be seen in the sky from Earth. So this example fails the only detectable by gravitational waves test.
However, what this example does is set out the parameters that need to be meet. However, there are factors that cannot be readily determined. Assume a spacecraft that is sufficiently massive, which exits hyperspace in a manner that is effectively an acceleration and acts a source of gravitational waves, the key question is can it generate a sufficiently strong enough burst of gravitational waves to be detected?
Fortunately, the spaceship will be exiting hyperspace close to Earth, so proximity of the source to the detectors is in their favour. Now gravitational wave detectors are incredibly sensitive instruments. On the other hand, gravitational waves themselves are incredibly weak which is why LIGO and other GW detectors are so mind-bogglingly sensitive.
This puts us in the realm of speculation, because we don't know exactly how strong any gravitational waves generated by a spaceship exiting hyperspace will be. In a work of fiction, the author can optimize the factors to ensure the alien spaceship could be detected. But if the author of this answer had to guess, he would guess against its detection. The gravitational waves wouldn't be strong enough.
The mass of the spaceship would have be absolutely massive. Its exit time from hyperspace has to be close to Planck intervals. Both the proximity and sensitivity of gravitational wave detectors need be better than existing devices. So, possibly future detectors will be good enough. if all these factors are in the right proportions, then yes it can be done, theoretically, at least, but guaranteeing requires dramatic licence and every fiction writer should have one.
Plausible, yes, Possible, uncertain.