I just went through the same process and landed in a very similar place, with almost the same list. (And for the same reason -- deeply unimpressed with 2d20 and Star Trek Adventures.)
I based my changes on what we see the characters do in the show. Thus I deleted Computers, on the grounds that the usage and operations side of this skill seem irrelevant in the show -- everyone can use and program them with ease -- and the construction and repair side is covered by Engineering [INT], which replaces Mechanics. Engineering is everything we see Scotty, LaForge, Torres and O'Brien do.
I dropped Driving and Astrocartography (which becomes part of Helm/Conn [INT]), and I merged the two Ranged skills, but kept Piloting [AG] for small craft.
I kept Operating but called it Starship Operations [INT] (i.e. Ops), which is essentially operating sensors, transporters, holodeck programming, tractor beams, remodulating shield frequencies etc. Basically everything you see Harry Kim do. Engineering is distinct from this in that it involves fixing and modifying said systems.
I added Science as a knowledge skill (Spock, Data), as well as History/Archaeology and Law (both for Picard ), all [INT].
I added Animal handling [PR] and Investigation [CUN] (for Tuvok), EVA/Environment suit [AG] . Instead of Gunnery I have Starship Tactical [INT].
I thought about but rejected a Gambling or Gaming skill -- you could just use Deception.
All other skills I kept.
Now I'm working on species archetypes, careers, equipment and ships.