I don't like Wookiepedia's use of the term "wrinkle" (which I don't believe is based on any canon source, though I could be wrong) because it has different implications than the way hyperspace travel is conveyed in all official Star Wars media I've ever seen/read/played/etc. I would suggest not trying to think of hyperspace in terms of wrinkles, because I don't think George Lucas ever intended us to think of it in wrinkles and the term "wrinkle" certainly isn't used in A New Hope, which is Wookipedia's "source" for that claim.
Hyperspace travel is analogous to real-space travel, but at different scales. You still have to travel through hyperspace - if the distance is further in real-space, it is also further in hyperspace. The films show that hyperspace travel is not instantaneous.
We also know from the films that it is possible to collide with real-space objects while traveling in hyperspace. In A New Hope, Han specifically comments on the importance of calculating the correct course before beginning a hyperspace jump, so that the ship doesn't hit an obstacle such as a supernova or meteor shower. Extended Universe sources further explain that each object in real space has a "mass shadow" in hyperspace that objects in hyperspace can collide with.
You can see what happens at the end of a jump in the films. The ship starts to appear in real space, but appears to be elongated and traveling at massive speed. In only an instant, the ship has returned to sublight speed and no longer appears elongated. I'm not sure whether this elongated effect is actual spaghettification or just a visual artifact of how fast the object is moving.
The following addendum is my interpretation and may not accurately reflect the universe: I tend to imagine hyperspace as a parallel dimension of realspace, where every object exists in the same position relative to each other, but something about the scale is different. Imagine if you shrank our universe to 1/1000th of its normal size. Then it would only take 1 year to journey between two planets that were 1000 years apart when the galaxy was its normal size. I don't mean that hyperspace is simply a smaller version of normal space, but that perhaps the concept of distance works in a fundamentally different way in hyperspace so that the limitations of the speed of light no longer apply.