You can get by without the tumbler. Washing the case lube off, and drying the brass will work. As well as washing to remove grit from fired cases before lubing, and sizing. I use a sonic cleaner most of the time, due the dust from tumbling setting off my allergies. Though I do use the tumbler still when I am in a hurry.
I got by for a year just washing them in soapy water, with a touch of white vinegar. Then rinsing, and laying them out in the sun on a towel to dry. Clean is fine. Shining brass is not needed for accurate ammo. Clean brass does not scratch dies. As well as the lube needs to be off of the cases before firing. Cases with lube still on them can spike pressure of the bolt face.
No matter how many times you do it and nothing happens it only takes something going wrong one time to kill you.