Thanks for clarifying that the decals are only shapes with no printing. Printed decals would be a bear to fix.
The vinyl surface will hold up pretty well to cleaning. The main issue will be keeping the cleaner away from the edges of the decal. Many cleaners will affect the adhesive at the edge, or even wick under the decal and affect more than just the edge.
There are a number of things that should remove the residue. There are adhesive removers like Goo Gone and similar products sold under other brand names. WD-40 often works. Rubbing alcohol sometimes works. You can try limonene (sold as a solvent or citrus cleaner). In a pinch, mineral oil or baby oil is likely to break down the residue so it can be wiped away.
Oily cleaners, like mineral or baby oil, Goo Gone, and WD-40, will leave an oily residue. That can be removed with alcohol or soap.
The problem isn't removing the residue, it's avoiding the edge. What is holding the decal down is probably adhesive that's similar to the residue you're trying to remove. You'll need to use very little cleaner so there's no free liquid to run where you don't want it. That includes if you need to clean off any oily residue after removing the sticky residue.
If the decal is flat, position it so it's level and gravity isn't pulling cleaner toward an edge. Don't apply any liquid directly. Put a little on a cotton swab (don't saturate the swab), and spread it very thinly on the residue, avoiding the edge. Give it a few minutes to attack the residue, then wipe it carefully so as not to get any on the edge. Repeat as necessary.
If this leaves residue along the edge of the decal, clean that in a similar fashion, but being very meticulous not to allow anything to go off the edge. Move parallel to the edge, going just next to it.
If any material, including softened residue, gets onto the seam of the decal, wipe it immediately. If the cleaner is oily, immediately clean the seam area with a little soapy water on a swab and let it dry.
Unfortunately, ensuring you don't affect the decal's attachment will turn a simple, quick task into a slow, meticulous one.
When you're done cleaning, if there's any chance cleaner got on a seam, let everything dry for a day, then inspect the decal edges to see if anything looks questionable. If you're at all worried that an edge may not be secure, you can seal the decal to the surface by coating it with a clear finish. Something like Krylon Crystal Clear Acrylic won't yellow. Apply a light mist from different directions to get it against the seam. Several light mists will seal the edge and smooth the transition so the decal is less likely to be snagged.