I loaded across more than a half-dozen different chamberings (including .223) for many years before I ever decided to buy a tumbler. Shortly after
I did... I began the process of kicking myself for being so short-sighted.
Tumbling the brass doesn't just get the brass clean, it removes colossal volumes of filth from your life. It takes dirt off your bench, off your ammo boxes, off your dies, anything that goes near your ammo, and it takes so much filth and schmutz off your hands and out of your life that I would suspend 100% of my loading activities if I were not able to tumble my brass.
So yes, you certainly can handload ammo without a tumbler (or more advanced case cleaning methods) but knowing what I know now... I would never consider that ever again.
As for trimming...
If you are loading bottle neck rifle, you will HAVE to come up with a method of trimming. The only possible way I could see successfully skipping case trimming for bottle neck rifle is the one weird scenario that I would guess you couldn't pull off:
If you had LIMITLESS amounts of once-fired brass, I mean thousands and thousands of pieces of the stuff, it would be possible to size brass, measure it, and see WHICH of the pieces stay within trim length tolerances and use only those. But that is a ludicrous answer to what is a very necessary step in handloading.
I will close this with:
If what you seek is to make decent, working ammo on an absolute shoe-string budget, we can help you with that! There are plenty of ways to skin these cats and doing it on a tiny budget is absolutely possible. Ends up being slower, more tedious and far more labor intensive, but you can totally do it and make very good ammo along the way. I made my ammo while I was in college on a budget that covered fast food, beer and gas money. It was the definition of a shoe string budget.