is relevant only to lack of lubrication. It's not "hypersensitive" at all. It's not overly sensitive - as you already know - under the foreskin because the foreskin slides so easily over it. Using the "flesh tunnels" with some lubricant should not be a problem at all - the lubricant lets them slide smoothly over the glans.
One of my concerns about the "Phimocure" site is their suggestions that the devices be used only for limited times and not at night. In fact (and bearing in mind that when used for stretching earlobes, they are used all the time), it is a process of "acclimatisation" where you try them in for an hour or so, then if comfortable for two hours, four hours, eight hours (you can of course, pee through them) and up to 24 hours, taking them out when you wash, washing the tunnel at the same time and rinsing it meticulously, and re-inserting.
Any problems, go back to shorter times, but the objective is continuous use.