Oil doesn't slow the curing of CA. In fact, it aids in the process, such as the oils in your skin causing it to harden instantly. On the positive side, it enhances adhesion. Oil penetrates the wood and CA bonds quite well with oil. If you're getting cloudy areas, it's likely due to a solvent evaporating from under it. For instance, if you wipe the cue with alcohol and run a coat of CA before the alcohol has evaporated entirely, you'll get clouds. As mentioned, it may also be a reaction between the CA & paper towel, especially if the CA is snapping off before it has a chance to bond with the surface. You may think about looking into something other than paper towel for leveling the finish, something more rigid & less absorbent so you can level/flatten the finish. Pen turners have only a couple inches of wood to finish. You have 29"+, and it has to be flat & smooth & flawless or else it looks terrible. It's only logical that your technique would be different than a pen turner's.
You wouldn't use a ball peen hammer to drive a steak in the ground, nor would you use a sledge hammer to drive a finish nail. Same basic principle, but different scale. A paper towel can be used to apply CA to a cue, but that doesn't mean it's the correct tool for the job.