If you use the search function you'll find several postings on installing a small "dorm" refrigerator in place of the stove and, alternatively, under the chart table. On the other hand, why not use the guts of the dorm refrigerator to refrigerate your existing icebox? That gives you refrigeration when you have shorepower or using an inverter or using it with ice. I got the idea from a previous posting on what used to be called the photo forum, which appears to no longer exist. My installation has worked flawlessly since 2004:
http://forums.catalina.sailboatowners.com/showthread.php?t=119304
Note, this will only work when you have shorepower or an inverter but you can still use ice. If you want true, 12v refrigeration, you're better of with one of the small conversion kits.
P.S. I don't know where I got the 1/1/21 date in referring to the original photo forum posting, must have been a typo.