A soft case is probably the best option. They provide the least protection, which can be an advantage when convincing a sceptical airline employee to let you take it on the plane with you, because it's obvious that it shouldn't go into the cargo hold with the luggage. They are far lighter than the other kinds of case, which is good because you're going to be carrying it a lot more. Packing Before you go anywhere, remove the handle from your instrument. Check that your case shoulder strap and its clasps are in good condition.
Some airlines only allow one piece of hand luggage.
This rule is flexible, and often has an exception for musical instruments. If you are flying on an airline that is particularly sticky on this issue, just take your instrument as your carry-on piece. At the center of travelling with your hurdy-gurdy is attitude. If you are confident without arrogance, you are doing them the favor of choosing their airline to meet your special needs. The first line of defense is to simply avoid the question of whether you can bring the instrument on board.