Dry fire. Slowly.
Lots of people have trouble transitioning from single-action auto shooting to double action revolver shooting, especially when they pick an airweight.
Nothing wrong with the gun, I have a 642, your 637's hammerless sibling. I have a CZ75 and a Makarov, too, so our gun choices are very similar.
I have seen people at the range with a double action that they aren't used to, especially when they are used to a short, light, single-action trigger, reach into the trigger guard and yank the trigger back all in one panicky move because the sights were aligned for an instant and they wanted to make sure they got their shot off while it was lined up right. Of course, yanking the trigger just yanked the whole thing out of alignment worse than it ever was, wobbling out there at the end of their arms.
Not saying you're doing anything that dramatic, but ... you may well be doing something similar in a smaller way.
So, dry fire. Put your finger on the trigger. Slowly roll the trigger back until the hammer falls. Don't single-action fire this pistol at all, at least for now. Treat the trigger like it's on ball bearings, and you're trying to get it to roll smoothly across them. Let the hammer surprise you when it clicks. Don't watch it, watch the front sight. Don't let that front sight move. Align it on a spot on the wall, on a light switch, or a target you have pasted up. (You're going to check 3x to make sure it's empty first).
Roll through that double action trigger over and over. Don't let the front sight move. Do that 50 or a hundred times, take a break, and do it again.
Then do it again tomorrow, and every day after that. Don't go shoot your gun again until you've done that 1000+ times. Get that picture in your mind - I slowly roll this trigger across these bearings, and the front sight doesn't move the whole time. With all that practice, your trigger finger will get just a bit stronger, and develop more stamina and control. You'll need that later.
See, you're training your brain, as well as your fingers and hands. Once you've got that 1000+ repeats of the correct action, go shooting. Set up some targets, pretty close, and shoot a few rounds through your gun. Your trigger control will be much improved, and your mind and hands won't let that front sight move - nothing different is happening with your live ammo, except that there's a bang after the hammer falls. Your fingers and hands and eyes and brain do everything the same before that.
Once you know you can hit with it, you can extend the range, start practicing rolling that trigger faster so you can shoot your defensive revolver faster, like in an emergency, and start training yourself how you would fight with it.
Have fun with it. This is some work, but you can do it!