Actually, I think the shutter on the Altix is fairly straightforward to access. The front lens assembly should unscrew quite easily, which then gives access to the front of the shutter. Here you'll find a securing ring or for some Altix models a circlip-type ring, which holds the speed ring in place. This page by Rick Oleson Synchro Compur will give a good idea what it will look like. Just some lighter fluid on the timing gear (aka speedcam) may do the trick, but I prefer to take it out and clean it separately, as its easy to drown the shutter in fluid and spread grease everywhere. The shutter blades should also be visible, if they are not clearly greasy I would stay away from lighter fluid/naphta for those, as it may just stain the blades. From the symptoms you describe it sounds like the speedcam rather than the shutter blades causing the issues.
If you have never done this but want to learn, I suggest to get an old bargain camera with Prontor-S or Pronto shutter, they are easier to work with than the Compur-style shutters.
If you are interested more about Altix cameras have a look at my website: http://www.cjs-classic-cameras.co.uk/altix/index.html.