The best move the EU can do to resolve this crisis is to just let in all 4,000 refugees. They could then be resettle them across Europe, and the EU could broadcast images of refugees living a better life than most people are in Belarus.
As easy as that choice seems to be, it will never happen. The EU (and the European voting public) is too anti-immigrant to tolerate something like that. But 4,000 people is drop in the bucket of a union with a population of 447 million. Admitting them would have no effect on employment or the overall economy. And for Europeans who just think foreigners are icky, they can rest assured that almost all of them will never even encounter any of the refugees if they were let in. But the fact that there is almost zero cost to the EU by admitting the refugees and it would give an enormous propaganda victory to the Union that would almost certainly get Lukashenko to stop piling refugees at the border, doesn't matter. This crisis is caused as much by the EU's bigotry as it is by Lukashenko's border shenanagans.