I am currently building my own Traveller universe, which is a little bit more cyberpunk-oriented that the OTU - though by no means, all-and-out cyberpunk; just more "Aliens"-style megacorps and more realistic development of computer tech (i.e. hand computer available, as IRL, in late TL7/early TL8).
That said, cybernetics should never be allowed to break the game, or even to rule the setting - for that there are CyberPunk2020 and Shadowrun (Great games, but they aren't traveller). Cyber is a flavor thing - if you want that flavor at all in your Traveller game. For example take these ability gains during chargen. Instead of saying "I had some heavy lifting during that year in the Marines and it got me a +1 to STR" you could say "I had an artificial muscle augmentation implanted in me during service". Make that Chromed cyberhands (with a back/shoulder enhancement to carry the additional physical stress, ofcourse
) if you want it to be less organic.
A +1 to STR is a +1 to STR, but a cyberarm or bio-enhanced muscle fiber implants gives a certain flavor to your setting, while physical training gives another; it doesn't break the game, it doesn't even mean much in metagame terms (especially if it's organic or semi-organic and thus harder to detect), but it allows you to set a certain feel to your game.
Also, think of equipment such as respirators or IR goggles or even, in higher TLs, a hand computer - implanted versions, which will cost much and will take time to be implanted, not to mention expensive maintainance, won't be totally unfeasable - it's a matter of feel and 'atmosphere' rather than of breaking rules.