Most of what it takes to do this is obvious. All of the best non-violent tools, sidewinders, stealth shields, etc. But 3 things made it happen for me.
1. Get a character with Ghost Vow and Unambitious. Makes the whole thing much easier.
2. Offworld Angel and a wrench. So many times while building your toolset and saving money, your mission requires you to take a dangerous route back out, sometimes with a rescue. Just set them down near a window, hit T to enable throwing your tools, then throw your wrench out the window. Then pause and the offworld angel will happily scoop you up and erase any damage.
3. Be willing to abandon missions. Once you get a look at the layout of a ship, if the route is too ugly, bounce out and go get a new mission.