Jof, I too think a plane is your ideal solution here. Planing can be an inexpensive, relatively quick and frankly very satisfying way to do what you need, very quietly too. And it will produce minimal dust, although if you're like me you will be repeatedly amazed at the volume the shavings will take up even working on small pieces.
IMO you don't need more than plane. It is perfectly doable to outfit yourself with a 4 and a 5 for reasonable money, buying new or vintage, but more than a few of us have done quite a bit of woodworking armed with only a no. 4. It's the ideal place to start anyway, if needed you can always get another one in due course.
I wouldn't give too much credence to the ideal that you have to have a proper bench to be able to use a hand plane! And not just for the size of the work you're asking about here either – there's a long tradition of kitchen-table woodworking among amateur woodworkers, going back all the way to the 19th century. But if your kitchen counters have the right shape you can do all your planing there, on a planing board or bench hook of some sort which can be a very simple affair and work perfectly.
Nobody has specifically tackled the end grain for some reason and while you can plane this perfectly well with non-specialist plane like a standard no. 4 you may not need to. You can get what I'm sure would be a perfectly acceptable surface for your needs directly from a hand saw, especially one with Japanese-style teeth as these tend to leave a particularly good surface.
To get very straight and square cuts you can buy or build a mitre box, or simply clamp a guide piece to the surface of the wood being cut and the saw can bear against this as you saw.