Here is a biscuit recipe that is typical of those made without a mixer. This is a richer recipe than the usual beaten biscuit recipe. From American Heritage 1964.

SHORT BISCUITS
2 cups all-purpose flour (or pastry flour)
4 teaspoons baking powder
1/2 to 1 tsp salt
1/2 cup cold butter
Milk
Sift flour, baking powder and salt into a bowl. Add butter (straight from fridge) cut into 4 or 5 pieces, and work into flour mixture with a pastry blender or 2 knives until butter is about the size of peas. Add cold milk, a little at a time, stiring it with a fork. Use only enough milk to hold the dough together. The less you use the better the biscuits. (We use low fat milk, 2% butterfat milk)
Now work the dough together with your hands until you have made a ball and all the flour is worked in. Roll dough about 1/2 inch thick on a lightly floured board, cut with very small biscuit cutter (we like them about 2 to 2 1/2 inches in dia.), and place on an ungreased cookie sheet. If you have the time, refrigerate the biscuits for an hour or so. Bake in preheated 450 degree oven for 10-12 minutes or until biscuits are lightly browned. Serve hot with fresh sweet butter (or apple butter or ?). Makes about 20.

The closest I have found to American biscuits are some of the simple scones from Scotland.
I will follow this with a beaten biscuit recipe from the same source.