That is the whole point, you don't need that much space to "Do it right", particularly if you are loading for just a couple of calibers.
I built something like this (found this photo online), just a little smaller:
I boxed the bottom under the lower frame rather than the top, so it made a nice storage area, it was light enough, even with tools/dies and components in the bottom that you could pick it up and carry it wherever you needed to work, then fit in the bottom of a closet when you were done, it was short enough to fit under hanging clothes.
You may have other reasons for not wanting to start handloading, but "I don't have space" is not a valid reason, unless you are some sort of hoarder and don't have room for a ~2' cube.
It simply doesn't take that much space, and aside from a drill and a couple wrenches to bolt the press down, you don't even need much in the way of tools or for that matter, carpentry skill to build it. I posted a bill of materials in the thread I linked earlier, just go to Home Depot and have them cut the wood for you, all you have to do is screw it together.
And that is just to build a bench like I did, certainly not the only way, do a Google image search for "compact reloading bench" and "Apartment reloading bench" you can get lots of ideas, there are a couple of what look like table-top benches people have made, a small box that you set on your kitchen table, and put away when done.