I believe your best bet is probably to use your jetbike to shadow ships.
The high speed of the jetbike makes it fairly good at tracking ships to their landing sites, even if it's completely unarmed. A lot of early landers aren't fast enough to do that, they'll often lose the target once it clears radar range of your bases. If you throw a Hand onto the jetbike, it'll stop and give you the option to land, pausing the game and allowing you to send out a real lander.
Honestly, I only use the charger laser on my jetbike to shoot down civilian ships; most of my real scores come from landing zone tracking. Knock over a few small ships and you should be able to get some light ship weapons together, even if it might be a bit before you can research them and reproduce them at a workshop.