Many overhead throwing athletes find that pitch accuracy, speed, and endurance can be compromised by injury and/or recovery after reparative or restorative surgery for that injury. And as you already know, overhead throwing (i.e., pitching) requires a fine balance between movement (mobility) and stability (keeping the shoulder in the socket). The perfect pitch doesn’t come back immediately after surgery without considerable rehabilitation and practice.
In fact, among elite professional (major league) pitchers, only about two-thirds (68 per cent) even make it back to the mound. The rest find it necessary to retire earlier than intended. Treatment under the care and supervision of a sports physical therapist is often recommended. Rehab may take weeks to months to iron out the kinks such as the “wobble” you mentioned.
The physical therapist will assist you in regaining normal shoulder motion, kinematics (movement), and proprioception (joint sense of position). To regain your pre-injury pitching performance requires careful attention to all the components needed for pitching velocity (speed) and control. And even then, according to studies, there is a chance that you will never regain all that you lost or return to your pre-injury level of performance.
Still — it is worth a try. What have you got to lose except maybe that “wobble”?! Based on studies published on this topic, you can expect recovery and rehab to take many weeks to months. Some players report a gradual return of their abilities and pitching performance over a period of two to three years.