I assume that the surgery being considered is plication of the diaphragm. The surgery cannot be done non-invasively. However it can be done relatively non-invasively by video assisted thoracoscopic surgery (VATS). Significant morbidity can be avoided by performing the surgery in this way. Improving your shortness of breath cannot be guaranteed, but there is a good chance of it.
Most importantly, the surgeon who does the surgery should be experienced in both VATS and plication of the diaphragm. Before agreeing to surgery it would be important to work with your doctor to be sure there aren’t other heart or lung problems causing you to be short of breath with exertion. A fair number of people with paralysis of one side of the diaphragm do not have shortness of breath. However, a person who is physically active like you is more likely to be short of breath from the paralysis.
The indicated procedure (if any) for a given individual depends on a range of factors. Consultation with your pulmonary specialist and your surgeon is essential for a final judgement as to what is best for you. My comments to dsgksg on September 22 may be of interest. I thought you might like to hear from someone who (at age 64) has, "been there, done that".