On a sporty bike it’s even more important to secure yourself on the bike with your legs, more so than on a more relaxed bike (e.g., a cruiser). Really take that to heart and try to loosen up your upper body as much as you possibly can.
Also, you really don’t need to give the bike much throttle to keep it stable in a corner. At the very least, get on “neutral throttle” (not accelerating but also not decelerating). Ideally, however, you want to judge your entry speed such that you can actually be accelerating slightly (slightly, not full-on) throughout the corner.