I don't blame you for being skeptical. I would want to know for sure too.
You're right about week 4--instead of taking it off and having your period, you put a new one on right away--but I think you have to continue with the next two for the following two weeks, so instead of having your period one week late, you'll skip it for an entire month. After that, i'm not sure if you can have your patch-free week or if you should continue with another new set of patches, because I always hear about people skipping their periods for three months at a time. It might work for two months, also, but i'm not sure.
This can actually be done with any monophasic birth control. It's usually done with pills, but it works with the patch too. You've probably heard of seasonale, the pill that lets you have a period every three months instead of every month. The only difference between it and other monophasic pills is the way it's packaged. It comes in a pack with twelve straight weeks of active pills, and then there is one week's worth of inactive pills, and that's when you have your period. If you skip your period with another type of monophasic pill, you skip the week of inactive pills and start immediately on the next pack of active pills. It's the same way with the patch or the ring--you skip the patch-free or ring-free week and put a new one on right away. I have used seasonale myself, and I have also skipped my period using the patch, so I know it works. You might have a little bit of spotting, but you might not. If you would be more comfortable doing it the way you originally planned--skipping your last patch and having your period the week before your vacation--that might work too, but I don't know if you would still be protected. Maybe someone here knows, or you can check with your doctor...Sorry, i'm just not sure. But the only problem I can imagine you having if you delay your period is the possibility of spotting. Other than that, it's no problem, and it's totally safe.