The obvious solution is to keep his feet off the ground except when stopped, and pull himself along by his hands. On Phobos, of all places, this is made easier by the grooves and striations on the surface.
It doesn't seem likely that there would be natural handholds on Phobos. They'd have to handle a lot of force for our fugitive agent to maneuver quickly across the surface. But since we haven't yet been to Phobos, there's no way to know.
Edited to add: I suppose one way to move across the surface is to push yourself horizontally using boulders big enough for their inertia to keep them more or less stationary even if they're just resting on the surface. Stand on the side of a big boulder (or lay on the ground with your feet against it), slowly crouch down (walking your hands against the surface) and push off horizontally towards another big boulder. Chances are you'll miss it and will have to wait to fall back to the surface so you can slowly make your way to another big boulder and repeat the process.