Any synonyms for "left" and "right"?
Solution 1:
I'm afraid the synonyms are more ambiguous, not less: dexter and sinister, when used in heraldry, actually mean the opposite of "left" and "right", i.e. while dexter is technically a synonym of right, it means the viewer's left, and conversely for sinister. Thus, if you said something like "the dexter part", apart from sounding very strange, you would have told your reader absolutely nothing useful about what side you meant.
Plus, sinister is so closely associated with its other possible meaning ("evil, ominous") that it would be distracting to find it used in a technical context.
Left and right remain your most unambiguous choices. If needed, you can add "hand" or "side" ("put tab A into slot B on the left side of the assembly").
Solution 2:
I definitely would not use Latin sinister/dexter or nautical port/starboard in IT technical documentation.
Firstly these terms have different meanings due to point of view.
Medical terminology has a tradition of using Latin, and these are known terms that have been learnt.
Port/starboard is just going to confuse your reader, they have no place in IT documentation (unless you're documenting [aero]nautical software).
Without any examples, my general advice is to stick to left/right and make the context clear you don't mean remainder/correct.
Solution 3:
For technical documentation I'd go with "left-hand side" and "right-hand side" - terms that are both commonly understood and unambiguous.
Solution 4:
At issue, if you had language alone there is no way to explain to, let's say, aliens which side is left and which side is right.
Since there is, save the radioactive decay and rotation of particles within weak nuclear forces, nothing with broken symmetry. Unlike colors where people get the words from objects around them (yes all colors, all languages), there's variation here. Notably some cultures have south-hand / north-hand (as in the hand closest to the north direction) or mauka side / makai side (mountain side / ocean side) in Hawaiian.
Though, it's fine. Chinese has right and left, zuǒ and yòu as in the left side and right side of the person talking.