Other options would be to use grips with a straight taper; OD is same length of grip whether standard or midsize . My personal choice is a standard grip with 2 layers of build up tape starting 4 1/2 to 5 inches from the but end of club (about 10″of tape). I have smaller hands. This has worked very well with my right hand, especially with wedge play. Britt explained very well concerning the effects of feel and grip pressure.
The old theory that larger grips restrict wrist pronation that can cause hooks is not always accurate, but some still promote it. Grip sizing is all about allowing you to grip the club comfortably, with the correct grip pressure, so that your hands can work as they are suppose to. What happens to a player that has grips that are too small? They squeeze tighter and that can actually cause the ball to go right (right handed player) because it tightens all the muscles in the hands and forearms. I have players go to larger grips that enable them to relax their hands and have the proper grip pressure actually reduce right shots because their hands and forearms are more relaxed. So, it really is about getting the size that feels right for you and allows you to grip the club with the proper grip pressure. It could work for you going to a larger size, but you’ll just have to try. It is not a given that going to a larger grip will automatically prevent a left miss.