Methods of quickly and easily implanting a quick-connect heart valve prosthesis during a surgical procedure are provided. The heart valve may include a substantially non-expandable, non-compressible prosthetic valve and a plastically-expandable frame, thereby enabling attachment to the annulus without sutures. A system and method for deployment includes an integrated handle shaft and balloon catheter. A safety member disposed between the balloon catheter and handle shaft prevents premature catheter advancement prior to heart valve placement at the annulus, and also may prevent premature balloon inflation prior to full catheter advancement.