This is simply a video demonstration on how to do this. Everything in the video will be covered bellow to make it easier to follow. All programs needed are optional.

You will want to use C:\Program Files (x86)\Steam\SteamApps\common\Space\spacegame\Config\

and the file you are looking for is DefaultInput.ini Everything else is the exact same.

I recommend using Notepad++ to aid in editing the ini files. It can be found: http://notepad-plus-plus.org/download/v6.7.4.html

Step one is locating the proper files the key bindings are saved to.

Navigate to
C:\Program Files (x86)\Steam\SteamApps\common\Space\spacegame\Config\

Step two is to locate the "DefaultInput.ini" file

Step three is to right click the "Defaultinput.ini" and select "open with" then select notepad (or notepad++ if you installed it).

This part might be tricky.

In each listing there is a "key=KEYNAME" all you need to do is replace KEYNAME with the name of your key.
The names of the letters in the english alphabet simply replace what's there. If you wish to bind to a mouse or numbers please follow the guide bellow.

1 - one
2 - two
3 - three
4 - four
5 - five
6 - six
7 - seven
8 - eight
9 - nine
0 - zero
Mouse 1 - LeftMouseButton
Mouse 2 - RightMouseButton
Shift - RightShift
Control - RightControl

If you have any questions please ask, I'll be more than happy to answer them.