In 2019 two plot holders on our site Wally and John grew water melons out on the allotment and not under glass. Looking at the RHS Web site re Melons it states that there are three groups of sweet melons. Canteloupe melons, with their orange flesh are the best ones for us to grow in the UK. You can also grow honeydew types, which have firm yellow flesh, and musk melons, which must be grown in a greenhouse.
Now I’m not sure how a wall can be sunny and sheltered at the same time.