The Variags were part of a regiment stationed in
Osgiliath (Which had been taken from
Faramir) and were originally intended to take part in the sack of
Minas Tirith. But of course, the original plan (thankfully!) failed and they were called in by Gothmog to aid the
Haradrim. Some of these went to aid the Haradrim (Who outnumbered the Rohhirm about 3-1) against the
Rohirrim and positioned themselves behind the Rohirrim and some attempted to intercept the force under
Imrahil that was attempting to aid the Rohirrim in their plight. When the Morgul host saw the
Ships of the Corsairs in the control of their enemies they began to loose hope and the regiment (Which contained some Variags) that was sent to intercept Imrahil's army was routed. The passage doesn’t say that they fled from the sunlight, but that the Orks hated and fled from the sunlight. The Variags were simply being driven away by Imrahil’s force from Minas Tirith.
The sun had been shining for some hours before, so that wouldn't have had a detrimental effect upon the Variags.
Also, do you think the slaves of
Mordor who lived on the Lake Nurnen were mainly from Khand? (Hence it being marked on the
map.) They seem to be the closest country to South-East Mordor.
Aragorn, of course gives the land about Lake Nurnen land to the former slaves of
Sauron. (Although from the passage in 'The Land of Shadow' it seems that Sauron recruited his slaves from a lot of different countries, not just Khand, but Khand seems to me, due to it's close proximity to Mordor, to be the most likely place whereby slaves are brought in from.) We also know that Khand had allied herself with the Wainriders when they attacked
Gondor and when Ondoher, Artamir and Faramir were slain and a new line of
Kings, under Earnil II, who was based at Pelargir and who defeated the Southern Army at the River Poros and routed the feasting
Easterlings.