Here are a couple comparison shots that may help a wee bit.
The first image shows (from right to left) the original rubber grip on my M&P 340 -- might be the same one that came on your 637. Next is an Altamont rosewood combat. And finally the Karl Nill Centennial model -- it's the biggest set of stocks I've seen for a J-frame. I carry my 640 Pro with these stocks everyday and everywhere, and it's a pleasure to shoot -- feels like a K-frame. This model won't fit on your 637 because it won't allow the hammer to go all the way back, but Nill makes a similar stock for J-frames with exposed hammers (same girth, just not as tall).
The second shot -- if you want to stick with rubber -- shows two Hogues. On the right is the Monogrip on a 360PD (same dimensions as your 637), and on the left is the Centennial Tamer, which, again, won't work on a revolver with an exposed hammer.
Hope this helps.
7-stud. Nothinís wild. Cut?