How can I plane the edges of plywood?
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.