About all 32 S&W is good for is plinking and yes that Safety should shoot just fine. Keep the target close and don't shoot at anything hard or you can get the bullet coming right back at you. I was about 10 when my grandfather let me shoot his 32 S&W. I tacked a paper target on the side of an oak tree and shot once as it bounced right back and hit me in the knee. I only learn from experience!
Another thing I learned many decades ago is that the trigger pull on these Safety revolvers is really quite good if you take some time learning the break point of the trigger. One has to aim, then pull the trigger back until you feel it stop. Any further pull fires the gun, so with a little practice you can hold the trigger just at the break point while you aim, giving much more accuracy. Good luck.