What is the drone's range of operations?
Where the drone is, and what kinds of celestial bodies are nearby, will drastically impact the propulsion options available.
Things that will work everywhere are essentially limited to various kinds of reaction wheels and photon drives. Reaction wheels are great for changing orientation, and pointing the photon drives, but won't actually push you anywhere. While there are a few far-out options being investigated, e.g., by NASA's Breakthrough Propulsion Concepts program, there are currently no other propellantless propulsion systems available within the realm of known physics.
However, if it has intermittent access to starlight for power, might it also have access to stellar wind? If so, the drone may be able to use a magnetic sail for both propulsion and breaking. Unless you have a large array of magsails, thrust will always be away from the source star in that case--tacking against the wind, like you can do with a solar sail, doesn't work so well with magsails--but that can still be useful, especially if the drone is intended to engage in interstellar travel, and needs a cheap way to decelerate into a target system, and a boost for leaving a source system.
If the drone is ever in the vicinity of a planet with a magnetic field, or sufficiently close to a star to make use of the star's magnetic field, then the probe could use an electrodynamic tether both for propulsion and breaking (in which case, it would generate excess power, which could be directed to a photon drive or for other purposes). This would be most useful for spiraling in towards or out from the host planet/star. If the drone is capable of giving itself a net electric charge (for which a simple electron gun would suffice), then it could manipulate its charge to generate turning forces in magnetic fields as well. This would even be useful for interstellar navigation (perhaps more so than for maneuvering around a planet), if the drone has access to a reasonably good map of the interstellar magnetic environment. Turning in the galactic magnetic field by charging the ship is an approach that has been considered for some interstellar exploration mission designs as a means of allowing the ship to approach the target star "from behind" and thus make use of a laser sail, powered from the home system, for both acceleration and deceleration.
When the drone is in proximity to other large bits of matter (like asteroids, or comets, or the actual wreckage that it's actively looking for), there are of course plenty of "simple" mechanical options. It can crawl around, it can use shock-absorbing legs to break and "land", and it can push off with legs. A grappling device (or suite of grappling devices for different surfaces) attached to a Very Long Tether (possibly one which could double as the previously mentioned electrodynamic tether) may be useful for grabbing onto Stuff from an intermediate distance (say, up to a few hundred or thousand kilometers). Such a tether could also be used in reverse to allow the drone to steal an object's rotational energy and give it a stronger fling towards a new destination than it could achieve with legs alone.