Yes, you will need to remove the engine. Take plenty of pictures and vides. They will help when putting it back together. But hopefully you will get a complete engine to put back in if the gears are destroyed. That would mean that small pieces could be lodged in oil ports which would cause more problems later. If you are lucky, it may just be the actual shifting mechanism that is either broke or misalign causing it no to shift correctly into every gear. That won't require a complete tear down and will only involve the removal of the side covers. I've seen that happen of a few Hawks on here.
You may just want to try removing the right side cover to examine first.
Here's a link to the service manual.
https://drive.google.com/file/d/1C-W...usp=drive_link