I would recommend using "No Wet". It is not petroleum based and will clean, polish and UV protect the shield. THere are other brands that will also help protect it but like you said, stay away from petroleum based products as this could soften the adhesive and cause a real mess.
Mike, RVIA & RVSA Certified Master RV Technician
Amy, Dr. Assistant - Roxie & Mei Ling, four legs each
2000 Gulf Stream Scenic Cruiser 450 hp & 1330# torque
06 Saturn Vue, 06 Chevy Z71 4x4 & 2014 Corvette Z51 M7