5/16" dowels will make cups that have better acceptance...
"Many beekeepers make a mistake in believing that the most important feature for successful cell acceptance is the grafting of the larvae into the cells cups; but a far more important feature is that of making cells of the proper shape and size. The ideal cell would be as the bees build them, large inside, with a small mouth; but it is not possible, or at least practical for the beekeeper to make cells of this shape. Upon several occasions, I have given cells that had been accepted and slightly built out in the swarm box to a colony for finishing, when by accident it contained a virgin queen. Of course, the larvae and jelly were both quickly cleaned out. I have given one bar of such cells to a swarm box and two bars of our dipped cells. The bees seemed to concentrate all their efforts on the cells already worked on by the bees and neglected my dipped cells. The bees prefer to make the mouth of the cell just large enough for a worker bee to crawl into, and it is frequently noticed that sometimes in the workers haste to back out of a queen-cell when smoke is blown into the hive, it is caught and has to do considerable scrambling and kicking before it can get out. I find the best cell for practical purposes is one whose size is between that of the inside of a natural queen-cell at it's largest place and the mouth of the cell, this being five-sixteenths of an inch as given above. In our early experience, many of us, enthusiastic in rearing larger queens, sought to accomplish this by making larger cells; but being large at the mouth, the bees were loath to accept them, and it took considerable work on their part to build them over to the size they should be. When the bees get to work on the cells they mold them into the shape they want, regardless of the size and shape the beekeeper has made them. The smaller cells will give better acceptance than the larger ones; but do not for a moment imagine this cramps the larva and produces an inferior queen, for the bees enlarge the cell to suit their own fancy. For experimental purposes I have dipped queen-cells the size of a worker-cell, and excellent results were obtained. Cells larger than five-sixteenths of an inch are not accepted so readily as those of this size or smaller."--Jay Smith, Queen Rearing Simplified
http://www.bushfarms.com/beesqueenrearingsimplified.htm#DippingCells