Is that area bigger than it looks? Because it looks like about a square metre. Also, I’m not sure what you mean by ‘smoothing out’ as an alternative. You’re not going to be able to get tremendous smoothness on brickwork. Unless you render it, of course. You’re right that you’ll need something to apply the render with. I’m sure a professional would make a better job of rendering, and that it might even last longer, but all render has a limited life span, and £30 for cheap tools and materials is a lot less than you would pay for a pro job. Also, I’m puzzled why, if you get on with your neighbour, they would object to you attempting to making their half look less shit. I painted my neighbour’s flaking and shit looking window frame with their permission. Asking for it was the first time I had spoken to them.