This question has a couple of layers that require addressing, firstly in that material for swords were traded far and wide, even if completed swords were not, and secondly that there were "Vikings" serving overseas in placed like Byzantium through the vangarian guard.

On point one: there is direct physical evidence of the trade of goods along the Volga route during this period, including the sale of walrus ivory from the north and into the middle east, and in terms of glass beads ("ancient glass, an interdisciplinary study", Henderson, 2013), and silver and gold coins, in both directions. So we know goods were traded between Norsemen and the "middle east".

A good literary source is the 10th century accounts of ibn fadlan, who travelled from the Abbasid Caliphate up through the Volga and into Russia in 921. He accounts not only trade, currency but also social and religious differences ("black banner and white nights, the world of ibn fadlan", J.D Wilson, 2014).

A source by a geographer, al-Muqaddasi, in 985CE talks about the goods being sold by Norsemen to the Arab world, and among the good listed is both swords and armor, so the trade of arms and armor existed (at minimum) between "Vikings" and the middle east in that particular direction ("Trade, Travel, and Exploration in the Middle Ages: An Encyclopedia", Friedman & Figg, 2013)

The sources we have for the purchase of goods by the Norse are considerably more sparse, and must be assembled from archeological evidence. A key form of evidence is crucible steel, which was produced in the middle east, near east, central Asia and southeast Asia from around 300 CE onwards.

Alan Williams in his 2009 paper "a metallurgical analysis of some Viking swords" reports that group 1 ulfberht swords are made using hypereutectic (over 0.8%) steel with very low slag concentration, and are likely made of crucible steel. The hypothesised route by which this was acquired is the Volga trade route, though the actual forging of swords was performed in Frankish workshops.

It's worth noting that the inscriptions on these swords isn't the only way we know they were made in Europe - but also the metallurgy.

Classic hypereutectic crucible steel is handled in such a way as to cause coarsening of the cementite particles in the steel until they aggregate into cementite spheroids along rafts of steel rich in carbide formers ("key role of impurities in ancient Damascus steel blades", Pendray, Verhoeven and dauksch, 1998) and this causes a relatively tough, yet hard blade. The ulfberht swords don't have these structures in them, because they weren't heat treated in the traditional manner that crucible steel was in the regions where it was produced. Instead of being thermally cycled to cause the cementite to aggregate in spheroids, the steel was instead treated as bloomery steel and so the blades are largely martensitic with precipitated graphite.

We don't have strong evidence of Norse adoption of foreign military arms in their raw form, only evidence of the use of foreign materials in Norse weaponry, and indeed the purchase of Norse weaponry by foreigners (or the use of Norse weapons by Norsemen working for foreign countries as in the case of the vangarian guard).

The balance of evidence suggests that they were more than capable of purchasing pre-made weaponry if they chose to do so, as the trade routes existed and were already being actively exploited, but the archeological evidence indicates that the Norse preferred to purchase raw materials and have weaponry made according to their own specifications and preferences.

This answer is somewhat sparse (it's 5am, and my brain is weak) and I might expand on it later today after some more reading, to see if I can find any more archeological evidence non-european weaponry in Norse burials, but hopefully it at least shed some light on the trade routes at the time.