It's unlikely an issue of which brand of lubricant you use - wiping the pin down with bearing grease is just as effective. The point is to have only a surface film, not residual lubricant that will in-fact liberate from the hinge at some point.
But you state that the smoke is only noted on one side; assuming you applied and used the same lubricant and installed both sides of the cowl the same way, it's unlikely related to that, but it's more likely have some relative motion occurring in the hinge that ends up resonating at a high enough frequency to cause the "smoke", in much the same way a loose rivet does.
The key point here isn't to better lubricate the hinge and pin, but to stop the movement.
Also, are you certain it's not coming from some other source that's working it's way to the edge of the cowl and out? Have you wiped the smoke off and smelled it? Is there a hint of lubricant? It literally only takes a drop of oil to make the "smoke" you see.