"Rudy" wrote
About a third of the exterior of my house is very rough stucco wall.

Does anyone have a better suggestion?

Rent a sprayer from Home Depot

Folks here warned me away from a sprayer a couple of months ago. Too much
splatter, and so masking, required.

I tried an enormous foam rubber sponge from the car cleaning supplies
department of Wal-Mart. A buck each. Works better than the thick-napped
roller. I went through five of them for half the house.