You don't. Come back with a proper space suit!
This. The mission allows you to win by just showing up pretty much, the despawn penalty is only for not engaging the mission at all (however you only get 0 pts for aborting after you show up). If you want experience credit you'll have to shuffle your hands outside the ship for at least one turn I think, though that does potentially expose them to reaction fire.
To get any benefits from the droid mission you'll need space suits, and you'll need some kind of Laser weapon because thats pretty much all you can take out into space (the advanced launcher works, but thats even further down the tech tree).
You could do melee but I severely DOUBT that you will get close enough before being reaction fired on and seriously raped. I don't know how powerful their weapons are but you dont get armor* in space and they are highly accurate (plus you usually get 4 shots from them). Getting from your ship to the satellite is like charging the MG bunkers on Omaha Beach.
In fact its so bad that if you even take an Aimed Shot with your laser you're still going to take reaction fire, so you had better use snap shots (because it will reduce the amount of reaction fire you take, and these guys have often taken 2 hits from a lasgun to put down).
The benefit of defeating and capturing the robots, besides some basic building commodities, are the Nuclear Batteries they cough up, and the EMP grenade that you get to research because of the droids. Im not sure if the nuclear batteries can be used for anything down the road as I haven't got that far yet, but they're probably worth keeping around just in case.
Space Suits
Although its quite a climb up the tech tree and you cant buy space suits, there is at least one place I know of that space suits can be found:
Trader's Warehouses, sometimes there is a (singular) Space Suit drop in the loot. The problem is im not sure if these start showing up early on since I only started noticing it in 2nd year, they may be random seed.
There definitely needs to be
some way to get access to a space suit early in the game besides picking the type of codex for the menacing hull that provides a few.
The mission isn't that tricky if you have a good melee soldier breaching the room and slashing the inhabitants to pieces.
The lost spaceship map IS playable with rescue pods. The guild spacemen usually stick to inside the ship so you can often approach it without being fired on. Once you get there you're going to need to rush them with like 6-8 hands in pods just to "fumigate" them securely, it'll take 2-3 blasts from the nitrogen gun to put them down and considering the small jaunt to get into the ship you're not going to get more than one shot each. Make sure that you have your fastest (highest TU) hands ready to move all the way from outside into the cockpit and still fire on the guy in there (if you go into the ship and you see nobody, they are probably both in the cockpit which means you should probably go back outside the ship and wait til next turn to get them separated or both in the rear compartment).
Sometimes these ships just have drones though, and while im not completely sure, I dont think the nitrogen gun is going to work on them (their armor is too high).