There are a number of ice machines on the market - some are quite reasonably priced (around $200.) You fill them every 8-12 hours with an ice & water mixture, then a circulating pump sends the cold to a cuff wrapped around the surgical site. There are specific cuffs for several joints, including shoulders. My insurance covered the cost with a 20% co-pay. Some examples are Cryo-Cuff and Polar Care.
Others are quite expensive, but may be available for rental from a medical supply, and often covered by insurance of prescribed. They include a compression component which may not be helpful for a shoulder.
Since cold therapy is very useful for many weeks during healing, these devices are a wonderful convenience, maintaining cold all night without running to the freezer for a new ice pack every hour. The only downside is the need for a ready supply of ice. The icemaker in my old refrigerator barely kept up, but the one in my newer whirlpool supplies plenty of ice for 24 hour use and has some left for my beverages.