We'll need pictures and more information to answer your questions. Gretsch has used the same model numbers for decades in some cases so that doesn't really help. The Satin Flame type wraps were mostly prevalent in the mid/late 1960's and early 70's.
What type of badge is on the drum? Round would be from (roughly) 1969 and earlier and a stop sign shaped badge would be from 1970 or later.
Satin wraps tend to damage easily and it is very rare to find them in excellent condition. The majority will have cracking and crazing in the finish but usually look okay from a few feet away. Unless the wrap on the drum you have is completely "toast" you'd be better off to leave it alone as far as the value of the drum. Rewrapping or refinishing any vintage drum that is more or less presentable as is can only reduce its value. Usually quite significantly. You might consider selling the drum to someone who's looking for a snare in that wrap (there's bound to be someone who 's hunting for that matching snare out there) and using the money to buy something more to your liking than re-doing this drum.
People have had good luck cleaning these wraps with Scrubbing Bubbles cleaner and a toothbrush. That might get rid of the stains you mentioned.