Travelling with eMTN bike - air, ship, cargo etc???

[Shakalau]

I am planning a 4 month trip to N America from Switzerland with my e-MTB.
Airlines do not take E bikes.

Is my ebike considered a regular airline bicycle when there is no battery?
I assume it is just a bicycle then. Can I fly with it, without battery, as normal bicycle luggage?
I cant find anything on that subject anywhere.
(Bike weighs 21 kg without battery. Battery is a Bosch Powerpack 500).

I think I have a few options available, but someone else might have a much better knowledge, please help me out:

1) I could ship the bike and battery together or in 2 separate shipments via some cargo company, or DHL type courrier.
2) Assuming my battery-less bike is a airline allowed bicycle, I could ship the battery separately by itself, or buy a new one, or rent one in N.America.
3) Buying a new bike in N.Am is not an option for me.

Any advice and directions would be awesome, thanks.

 

[outerlimits]

It’s usually just the battery airlines have a problem with. I’m going to fly my bike without battery and hire a battery at my destination.