Bike store boxes have worked for us. No problem finding boxes last year in Paris but we did visit about 5 bike stores. Only one wanted to charge us.
Boxes also allow for a point to point trip vs a circle tour.
Some maybe all airlines have made shipping bikes much cheaper. You should check out their current policies. Lufthansa, out of NYC had a roll on program. We used that one time to and back from Europe.
Learn how to pack the bike. And know the size boxes that fit your bike. It will be helpful when you are searching for one at your final city.
have a great trip.