The density of the solar wind is (at a low estimate) about 3 protons per cubic centimeter. This means that a macroscopic object moving at $v = 0.99 c$ will be colliding with protons at an approximate rate of
$$
\left( \frac{3 \text{ protons}}{\text{cm}^3} \right) \left( 2.97 \times 10^8 \text{ m/s} \right) \approx 9 \times 10^{14} \frac{ \text{protons}}{ \text{s}\cdot \text{m}^2}
$$
or about $10^{15}$ protons per second for every square meter of frontal cross section of the object.
Moreover, you have conveniently picked a speed ($0.99c$) for which moving protons can pair-produce with stationary protons (the protons in the solar wind are basically stationary compared to those of the ship):
$$
p + p \to p + p + p + \bar{p}
$$
The threshold energy for this reaction is that the incoming proton must have energy of $E = 7 mc^2$, but for $v = 0.99c$ the protons in the ship will have $E \approx 7.09 m c^2$ in the rest frame of the Sun. If this process occurred, the subsequent annihilation of the antiprotons would generate large numbers of 938-MeV gamma rays, which I suspect would be easily detectable (given the proximity of the source) by satellites such as Fermi, INTEGRAL, or AGILE, and possibly by ground-based gamma-ray observatories as well. Even if the aliens tapped the brakes a bit, the reaction
$$
p + p \to p + p + e^- + e^+
$$
would still be possible, and the electron-positron pairs would then annihilate to emit 511-keV gamma rays. So this is a fundamental problem that the aliens would have to deal with.
If the aliens don't want their ship to ablate via pair-production during their voyage, then they need some sort of way to move the protons out of their way. But whatever technology the aliens have to do this, given the speed of the craft the protons will still have to accelerate rather quickly. They would thereby emit bremsstrahlung, which probably wouldn't be quite as easy to detect as $p\bar{p}$ or $e^- e^+$ annihilation but might still be quite noticeable.
