First off, you have not indicated that you have read the articles that the videos are only meant to supplement. So in case you haven't, start here:
viewtopic.php?f=15&t=1329What you need to worry about firsthand when you get the parrot is getting it comfortable with you and hand tame. Think about what kinds of physical manipulations you will have to do in order to get the harness on and tame those. With a new untrained bird, believe me, all the touching required will be the bigger issue than the sight of the harness itself. Kili was only scared of the harness cause I forced it on her the previous day and she didn't like it. So I had to start over and use positive reinforcement training to get her to wear it.
You can use the techniques in the harness article (minus the harness itself) to get your hands closer to the parrot, eventually touch the parrot, be able to open the parrots wings (to slip harness under), etc. The parrot must be fully confident in your touch prior to applying the harness. If the parrot is scared of you, it will also pass that feeling toward the harness and the harness will trigger fear in it.
Of course if you haven't already, be sure to check out my basics of
taming/training article. If you go through all the necessary hand taming and leave/show the harness to the parrot throughout all this time, by the time you are ready to put it on, it shouldn't be scared of it. Walk around holding the harness. Show it to the parrot (but don't touch). Leave the harness on the table while you are doing the basic taming/training steps. Then when the parrot is tame, I would still recommend following the procedures I used in the videos. You may achieve quicker success than I did with a scared parrot, however, DO NOT just assume and stick the harness on. The harness is uncomfortable at first and you will jeopardize all the work you did if the parrot isn't gently/pleasantly introduced to it.