At the end of the Battle of Stalingrad, the Sixth Army was split in to two pockets, North and South. Later a Central pocket was formed. The South and then Central pockets surrendered first. The Northern sector was the last to hold out in the city, until February 2nd, 1943. This was mostly made up of Generaloberst (Colonel General) Karl Strecker's XIth Corps . Some of the units under his command were Romanian, but mostly German.

Now the Stalingrad area airfields that were used be the Wehrmacht were Pitomnik and Gumrak Airfields. Pitomnik fell first in middle of January, and the ancillary Gumrak airfield was used until it fell, with Soviet tanks literally driving up and firing at fleeing planes, on January 23rd. So no it isn't possible that your Croatian uncle was at one of those airfields, as a free soldier, after the Battle. Now, he may have been captured at the airfield because he was wounded and trying to escape, but I believe I read that some of the wounded at Gumrak were shot, and the walking wounded were marched in to the city a few days after Sixth Army's surrender. He could have also been at one of the airfields just outside of the Stalingrad pocket, that would later evacuate as the Soviet thrusts widened.

Edit: However, after Sixth Army's surrender, Wehrmacht and German Allied soldiers (Romanians, Hungarians, Italians, Croatians etc...) were all over the place within the city itself and the open steppe outside of the city. The Soviets had to hunt everyone down. Some units put up resistance after Paulus gave the surrender orders on February 2nd, but for the most part most units were too exhausted and weak to fight on. Some areas went unoccupied by Soviets for a day or two, but the Axis soldiers were told to lay down their weapons and wait for the Soviets to come take them in to captivity. But 14 to 15 days after the battle was impossible, unless he was outside of the Stalingrad encirclement all together.

Some good books to checkout on Stalingrad and it's aftermath, from a more personal level are:

After Stalingrad: Seven Years as a Soviet Prisoner of War Book by Albert Holl

Survivors of Stalingrad: Eyewitness Accounts from the 6th Army, 1942-1943 By Reinhold Busch

The former is very daunting and detailed, and is truly lets you feel how the author felt. The latter book has several different mini biographical accounts of the battle and the aftermath. Remember all of the people who are quoted in that book were either wounded and escaped via plane, or were captured and spent years in captivity. So they have some very detailed personal accounts of the end and aftermath of Stalingrad.