I don't try to get an even coat, not even on chrome oxide - it's too easy to get sucked in to overapplying the paste if you go for evenness. I take a very small dab - about a 1mm-long line from the syringe - and smear it diagonally down the paddle at about a 45 degree angle. I apply the line sideways on my fingertip and slowly roll my finger as I rub it across the paddle to help ensure an even track across the paddle. I'll do about 4 smears in each direction (i.e. at 90 degree angles) resulting in a crosshatching pattern, then smear it lengthwise up and down the paddle as best I can. The first couple of razors you hone will smear it around even more, though you may not be able to see this because it's so thin. But it'll still work great. Using a thin coat reduces the drag and makes it easier to strop on the pastes using only the weight of the blade, resulting in a sharper edge.

I use the same technique for applying other abrasive pastes like coarser diamond pastes and chrome oxide, whether the substrate is leather, wood, vellum, cardboard or paper.