The way I read an understood the rules, there is a difference between "running" and "sprinting" as a movement option. Only the latter requires an actual "Running (Skill)" Test.
So, if your group decides to just "Jog along" at their base running speed (SR4A p.149), no running Test is required.
"Sprinting" requires a simple action and a running test (SR4A p.148,149) as opposed to merely a free action and no test for simple "Jogging" (SR4A p.149).
As far as fatigue is concerned in such a case, the rules specifically differentiate between Jogging (running without a skill test) and Sprinting (running with a skill test):
QUOTE (SR4A p.164)
Fatigue Damage
[...]A character can sprint for a number of turns equal to his Body plus the hits on a Running (Long Distance) + Strength Test before he or she begins to lose steam. If the character continues to run beyond this base period, he or she begins taking 1 box of Stun damage each Combat Turn from fatigue; this damage cannot be resisted.
If a character is merely jogging along at his base running rate instead of sprinting, the gamemaster should increase the base period to (Body + hits) x 2 minutes, and only apply 1 box of fatigue Stun damage each time that period passes (rather than each Combat Turn) The maximum amount of fatigue that can be taken is 6 boxes of Stun. After that point, the character must make a Body + Willpower (2) Test each Combat Turn (sprinting) or Body + hits minutes (jogging). If the character fails, he collapses from exhaustion and is simply unable to continue any sort of strenuous activity until he rests.
So, unless you need to go faster than your base running rate, no skill test is required and you can even run longer distances that way.
I hope that helps to clear up some confusion (assuming I read and interpreted the rules correctly).