Carrying over 10,000$ declared cash out of Canada or USA is not illegal. However, single men are likely to be sent to an interrogation room because of paranoia against single men.
It's mostly American men who seek advice from me about their move to mainly Asia, where they tell me that because of pro-feminist former US President Barack Obama enacting FATCA in 2009-10, dozens of financial institution in Asia are refusing American citizens to open bank accounts because of FATCA compliance issues.
In other words, many men who want to leave Canada/USA are stuck in a trap in regards to opening foreign bank accounts, because to hire a lawyer to open one can cost a few grand.
The only option for American men is Charles Schwab, but this implies that the American man must retain ties to the USA as he is using an American bank account....Some American men want to sever ties with America so badly that they are considering cancelling their citizenship....But this was back in 2014 & with Trump being elected as POTUS, American men I know aren't that desperate like before.
Plus, it's not that easy to open a bank account in foreign countries, because foreign countries are also forced to comply with FATCA, which nearly affects every financial institution in the world except for Switzerland, Cyprus, Isle of Man & a few other tax havens...However, traditional offshore havens like Cayman Islands & Panama are being forced to comply with FATCA.
However, because OP is in Europe, he has several options such as Isle of Man, Jersey, Luxembourg, or even an Eastern European financial institution which isn't paranoid.
As you said, OP can wire his savings from his primary Bank account in his country of origin to his foreign bank account that he anticipates to open, or if he finds an International-friendly bank in Europe to conduct worldwide ATM transactions at low or minimal cost, that's even better.