Below is the link to a PDF of a custom character sheet I have created for my campaigns in FASA Star Trek the role-playing game.
It is highly detailed allowing for in-depth character creation and is geared towards a TNG or later setting.
FASA Star Trek Custom Character Sheet
What skills you would drop from the master list if
you were running a game in the TOS era?
Mainly, just the Holodeck skills. Also, Galaxy Class starship would be Constitution Class.