Golf Pride Tour Wrap has been my favorite since the first time I was due for a new one because it is tacky and easy on the hands. Golf Pride- Tour Wrap came out with the new "2G", maybe a couple of years now or so, and they are even more tackier-er-est-ers. If you think you'd like to change to it, that's my bet.
Anyway, another reason why I like it is because it is very easy to slip on a shaft, even if you had to build layers. . . it's quick! I used to take my clubs to a shop for re-grip, but a few days and then picking it up . . . extra trip and time. It's the convenience.
Oh, GP-tour wraps are standard weight like your cords. If you'd like to experiment with lighter grips, those multicompound are a bit lighter and may give you a closer feel to cords. They cost a little more . . . and then there's Winn lites. . . I think they are even lighter.
But, go with what you like most and what you think you'll benefit more from.
(Any chance for us to see a picture of it after?)