Unless they were willing to go cross-country, which is probably not a good idea for a small party of guards with the organization's top commander, the Stormcloaks would have to pass somewhere near Darkwater Crossing if traveling between Windhelm and the Falkreath Stormcloak camp east of Helgen. Darkwater seems to be a natural choke point unless you're willing to travel far out of the way and head down towards Riften before cutting west. However, a longer journey means more time exposed to the hazards of travel.
The Rift is Stormcloak-friendly, so there aren't large numbers of Stormcloak troops hanging around there. They're needed out where the fighting is taking place, in the Falkreath and Whiterun camps. There is no Rift Stormcloak camp, but there is an Imperial camp south of Ivarstead and one in Eastmarch close to the Morrowind border. We know that the Imps staged a successful raid on Shor's Watchtower, probably out of the Eastmarch camp, which is far deeper in Stormcloak territory than Darkwater Crossing.
A bigger question is why Ulfric was traveling anywhere at that point in the campaign. Why wasn't he sitting tight in Windhelm? Bad intelligence? Did he not know that the Imps had established those camps in friendly territory?