My friend at BASF developed and commercialized a new shrink wrap based on an SBS copolymer (styrene and butadiene) which should be polar enough that you can print on it. PET shrink wraps should be too.
Also, what is the recycle-ability of the shrink wrap plastic? Has anyone started using bio-degradable plastics for shrink wrap? What is the cost difference?
It is recyclable as they are thermoplastics which you can melt and reuse.
As far as I know biodegradable plastics are not yet used. In general they are inferior to synthetic plastics, cost more and are less environmentally friendly too.