A block plane might work but you're going to have a very tough time taking down 1cm of wood over such a long length. If you do use a plane, go in small increments and make sure you keep your blade as sharp as possible.
A belt sander will work better, provided you use 40 or 60 grit sandpaper. Anything higher (smoother) and it will take you an eternity. My biggest caution with a belt sander is to be careful to work evenly. It's easy to get distracted and create a divot where you've sanded too much.
If the sanding is daunting or you want something with more precision, I would recommend using a handheld router with a flush trim router bit. This will get you a nice clean edge. I would try to get the board trimmed down to less than 1/4" overhang or so first if possible, with a jigsaw or something. Then clamp a long straight piece of wood along the line you want to keep.
If there's enough of an overhang to get enough stability for a circular saw and a guide, that would also work. But it sounds like the overhang is too small for that.
It sounds like you have a very sensible and thorough approach to the project. Just a few suggestions:
Saw Blade
Most blades that come with table and miter saws are fairly low end. If you are cutting plywood for finish carpentry, you want a high tooth count blade for smooth cuts. Check out one of the blade manufacturers for the range and you will find some recommended for this type of work. The cost is worth it and it will last through many more projects.
Angle cuts
This is where your cut-twice idea is a good idea. You are just trying to replicate a given angle. Measure the angles either with a protractor, or, if the piece being matched is an angle cut across a short dimension (rather than a long bevel) lay it up against the angled saw blade to check.
Use scrap wood to make a try cut angle based on your best estimate. If it is off, adjust the blade or angle guide slightly and try again. When you have the exact angle, cut the good wood.
If you need to make an angle cut on a wide board on the table saw, consider an adjustable taper guide that runs along the fence.
Materials
It wasn't clear to me whether you were going to make the face frames out of pine or just make mock ups and then use oak. For the actual frames, use oak. It is both more rigid and much less prone to seasonal change. All woods shrink and swell somewhat, even when well sealed, but softwoods much more so. You could find shifting of doors and binding drawers if you use a wood that changes much.
Cutting on/next to marking lines
It doesn't matter. What does matter is consistency. You need to know where your mark is in relation to the exact measurement, and cut accordingly. And do the same thing every time.
For example, if you measure a board using a rigid rule, and you mark with a pencil, you can have the far edge of the pencil line at the exact distance. The thickness of the line is within the length you want. Then make a line across the board using a square at the exact spot. Many woodworkers use a scribing tool instead of a pencil to get a finer marking. In this case, you would cut leaving the line behind, since it was within the length you wanted.
Also realize that when your finished cabinet meets other surfaces, such as the wall, it will almost never be an exact fit, due to slight irregularities in angle and levelness of the wall. This is where trim strips come in. While there is a technique for scribing an exact contour to fit a cabinet to a wall, that is a bit more challenging. Unless you are going to do that type of trimming, leaving a cabinet a hair shallow or short is much better than too deep or too high. Shims and trim work wonders.
Best Answer
Sorry. My first answer mis-understoood the question. Based on the updated question, there are many ways to create a shape of the desired profile, based on what tools you have or can find/buy/etc.
Very much depends on what tools you have, how much money you want to spend. You can use it to justify buying a specific tool, if you have a use for one of the tools I've mentioned. They are all useful.
A tablesaw or a router are both terribly useful tools, but if this is a one time job and you have no interest in woodworking, then I'd look for a friend who can help you out. If you insist on doing it yourself, and might have an occasional use for a hand held circular saw, then go that route. A circular saw will be often enough of use even to someone who is not an avid woodworker.
Attach your board to a straight piece of wood to use as a fence. Then angle the blade, and rip the edge as you want it. I'll argue this is the cheapest solution that will give you a good edge. (A hand held jointer plane might be even cheaper, since you can get them quite inexpensively from an antique shop. But a jointer plane will take some practice to do this job well.)