Sticky Polymer Question

I am looking for a company that can produce materials composed of an isoprene polymer (a synthetic rubber), styrene-butadiene copolymer, or a poly(styrene-butylene-ethylene) copolymer along with tackifiers or a melt blend admixture of poly (styrene-ethylene-butylene-styrene)triblock copolymer and plasticising oils.

Basically what I am looking for is someone that can produce the same or similar material as the sticky hand toy or wallwalker toy that kids throw against the wall but I need it in different shapes for different purposes.

These material needs to be pretty sticky and once these material no longer adhere to a surface, they can be washed with soap and water to restore the tackiness.

I'd appreciate any help.

Thanks,

Al