Yes, Fighter/Freighter skill impacts your traveling time.
If I am not mistaken it affects both Hyper and Sublight travel.
You can change the skill in the upper left corner. You will see a huge difference depending on the skill. But the hyperspeed of a ship will still have the biggest affect on your travel time. No amount of skill can weigh up for a fast ship.
Skill 1 HS 1
Long route takes 20 days
Skill 5 HS 1
Same route takes 17 days
Skill 1 HS 5
Same route takes 4 days
Skill 5 HS 5
Same route takes 3 days
So skill does not have particularly big outcome.
Go for a fast ship. But skill impacts RP value though ;)