In D&D, the main conflicts are environmental, interpersonal, and violent. Thus, the three pillars - exploration, interaction, and combat. Each class in D&D is designed to help a player approach all three conflicts and resolve them in a unique way.
It sounds like those wouldn't be the main pillars for a Trek-esque setting - if you can get away with being a protagonist there without being much of a fighter, combat is not an important pillar. Being able to fight is a "ribbon," a thing that maybe some people do for flavor. At most perhaps a skill you can take (Strength (Brawling)). This seems reasonable given my exposure to Trek - Kirk's sweaty wrestling sessions weren't essential for every character.
So I'd look at what the main conflicts you're looking to explore actually are, first. Internal? Political? Ideological? Technological? Emotional? What do Spock and Scotty and other non-fighters struggle with and use their skills to overcome? What threatens them? What are they afraid of?
Once you know that, you can use those as important pillars. I'd then make new classes or tweak existing classes so that your players could pick classes that fired on the conflicts relevant to your setting, rather than the D&D default ones. You might also need some resolution systems a little more robust than skill checks for these challenges, some failure states that are a little less binary, maybe even different ability scores. But changing a pillar of play is a pretty major change to the game.