For the half-courier process I can't give you a definite sum but I can give directional because of the Stockholm stop. We flew Chicago - Stockholm on SAS which allows them to ride together in a single crate. They had a large dog crate so had plenty of room, which I lined with a large super absorbant pad just in case of an accident (dryfur.com has all you need for pet travel). Not every airline will allow pets to fly together, so that may be something worth checking.
Chicago - Stockholm: SAS was SUPPOSED to charge us $600 to fly them, but I had to pay it at the airport and the check in agents were more thrilled with the cute kitties than remembering to charge me. I realised over Detroit we were never charged!
Stockholm - London: Animal Couriers quoted us £750 total for both, riding in a shared, specially outfitted pet taxi door to door (a 2-3 day trip). You would have to email for a channel quote, but I cant imagine it would be much more than a few hundred a pet.
For the flight, most vets will not sedate the pets and ours weren't at all. They were fine, if a little confused, at the other end, though I did worry about them all night. Overall they were in the crate for about 14 hours door to door: 2hr drive to Chicago, a few hours at OHare (we had to take them out so they could scan the crate - make sure you have a leash or some way to hang on to them!) and they were put in a baggage room before being loaded on last minute to the plane in the heated hold. 9 hour flight, hour at Arlanda, 1 hour drive to our destination where we had a litter box set up and ready to go.
What we DID do was ensure to take them on car trips so they got used to traveling together and riding in a moving vehicle. Now they love riding in the car, and I think that helped ease any anxiety for them. However, I really didn't want them to go through the anxiety of a flight (not to mention the cargo costs) so the road courier was the best option.
Every state has a USDA office, but this lays out all the information (much better than when we did it!) - https://www.aphis.usda.gov/aphis/pet-travel