Would an eruption affect shipping and the movement of oil tankers?
No, Redoubt is over 200 miles away from Valdez. The Cook Inlet is separated from the Prince William Sound by the Kenai Peninsula; they are very separate bodies of water.
http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=valdez,+ak&sll=60.743056,-148.985596&sspn=4.29693,11.975098&ie=UTF8&ll=60.478879,-149.0625&spn=4.332942,11.975098&z=6