On Friday, in an ATA shoot, I shot a 97/100 in singles and a 92/100 in handicap from the 20 yard line.
I shot a Parker VH, 32" barrels with 34/1000th choke in both barrels, single brass bead painted white, double triggers, 7lbs-11oz, 14-1/2 x 1-7/8 x 2-7/8 with an old Redhead pad.
Can we assume this is the old Parker that you wish to "improve" with a fatter grip?
You're going to give those guys with the Perazzi and Rizzini O/U guns a heart attack.
If you end up wrapping the grip with anything, I'd use shrink wrap or Saran wrap first to keep any type of adhesives from sticking to the remaining original finish. Maybe even some paste wax first as a release agent for the shrink wrap.