Just in case there are any new players reading this thread. I just hauled a couple billion isk of Thukker Cap Batteries to Jita through Uedama without any trouble what so ever. I wasn’t cargo scanned, I wasn’t targeted, I wasn’t ganked, I wasn’t shot with fire works or a snowball from a snowball launcher. I just warped to 0 over and over in my mastodon, and put my batteries up on the market in Jita.
Don’t let these fear mongers scare you. Learn the tricks and travel is easy peasy.