There might be skill-independent perks. I think there were a few in FO.
Except we have no reason to believe so. Everything suggests that
all perks will be tied to skills.
Health Can Replace Endurance.
Archery Can Replace Agility.
Weapon Skills can replace Strength.
Stamina can Replace Willpower.
Magicka can Replace Intelligence.
The Speechcraft Skill can replace Personality.
Speed is at a set figure, I'm guessing that the different races will have different run speeds like a Wood Elf will run much faster then a Nord.
Luck is useless and can be gotten rid of.
I tried to explain that in another thread:
What you forget is that every attribute governed several skills. Even the best marksman will now sneak like a drunken cow.
Attributes made sense because they added another layer of specilization: When you get stronger, you get better in all things that require strength; when you improve your agility, your get better in all things that require nimbleness; when you get more intelligent, your get better in all things that require intelligence. This is gone now, without any replacement.