If you have a design that doesn't involve cuts all the way around the edge of the disc you can manipulate the vinyl to wrinkle in the spot where there are no cuts.
It takes a lot of finesse sometimes to apply the vinyl to the disc. I'm jealous of sign makers, as most signs are 2-D. We have to wrap the vinyl around a dome, which causes the wrinkles near the edges you're concerned about. Any part of the vinyl that has transfer tape on it should go on wrinkle free due to the aid of the tape, but if you have tape on every square inch of vinyl it has to wrinkle somewhere.
Therefore, I advise you to apply transfer tape to only the cut areas of the vinyl, leaving the other areas to absorb the 3-D stretch by wrinkling. It is similar to the crumple zones they engineered into cars.
If you always have designs that involve cut areas all the way around, then you will have to develop some better application skills and learn how to stretch the vinyl during application in ways that allow it to lay flat without wrinkles. It's possible, I have to do it occasionally, but I can't really explain a technique to it- it's a feel thing.
We are not like those other golfers. We throw our clubs and keep our balls where they belong. -Ol' Bob