Howdy
You really need to get a tumbler. Now having said that, there is nothing wrong with just rinsing your brass and letting it dry. The real purpose of cleaning your brass is to remove any grit that it may have picked up. Particularly brass that has been ejected from a rifle and fell to the ground. Grit is fine particles of sand that is often present in any soil. Grit is extremely hard, and if it gets run through your dies it will probably scratch the dies. It may even imbed itself in a die. Once your dies are scratched, they will in turn scratch all the brass you run through them. So making sure to clean the grit off your brass is very important. Frankly, I would not bother with 409, I would just rinse my brass in some water with a squirt of dish soap in it. I do this for my Black Powder brass before tumbling it, but that is because I have to rinse away the corrosive BP powder fouling before it sits too long. You could do the same with Smokeless brass, rinsing away the grit while you are at it. However you rinse your brass, be sure to rinse it out with plenty of clear water to remove any soap or whatnot before drying.
Now shiny brass, is a completely different story. If you rinse your brass without tumbling it, you will probably not remove any powder stains. The fact is, shiny brass does not shoot any better than stained brass. Shiny brass is easier to find in the grass, and it looks real nice, but it does not shoot any better than brass which has simply been rinsed. Tumbling in a medium like crushed walnut shells is a very mildly abrasive activity, and it is the mild abrasive that shines up the brass. Tumbling will also remove grit, so it is good for your brass and your dies.
So either way, rinse it, or tumble it, so long as you remove the grit.
Personally, I never bother to clean primer pockets. Particularly with ammo that has only been loaded with Smokeless powder. If I was producing super precision rifle ammo for long distance accuracy, then I would probably decap and clean the pockets. Bit I would probably only be loading 50 or 100 rounds at a time on a single stage press. When mass procucing pisol ammo, I never bother to clean out primer pockets. There just is not all that much gunk down there. I simply dump the brass in my tumbler, tumble for a few hours, then spin the brass to remove the walnut shells and start loading. No cleaning of primer pockets.