Is there any way to fix pectus excavatum without breaking bones?

I don't think so: It's an anatomical defect, hence it must be taken care of surgically. I would not recommend it, though, just for cosmetic reasons only, as the outcome of surgery may not necessarily be cosmetically pleasant either.

Yes: The nuss procedure involves placement of a bar under the breast bone to allow it to reform and remodel. The bar stays for about two years. The operation is minimally invasive. You can google nuss procedure or heck out youtube for videos of the operation.