Don't adjust your wrist to bring the cue closer, bring your body closer to the cue.
Without seeing you play I have no idea how you'd go about doing this. I have 4 contact points with my cue; both hands, chin and my chest. If you have quite an upright stance you should have 2 points of contact.
I can't imagine just having my arm dangling at the side of me without my cue touching my chest, it feels so unstable. Make sure you have your back foot on the shot line, front foot out to the side or forward then bend from the hips so your head is over the cue, chin touching or a couple inches off the cue. Your upper arm should be aligned with your cue. If you do this your cue will automatically draw to your chest, and give your shooting hand plenty of clearance from the hips.
If you don't want to transform the wholse stance then a fairly simple transformation can be done to get the bridge hand, head, shoulder, elbow and back hand all aligned....
When you approach a shot with your arm by your side, push the upper arm into your side so no one can smell your armpit

keep this like that when you get down on a shot and all throughout the stroke. You will need to twist slightly at the waist so your chest faces your cue a little instead of the ground. It gives the feeling of pushing your shooting shoulder 'back' a little. This should at the very least align your cue with your upper arm.
Good luck,