The story
Likely from shoe in some way, if not a clipping of shoebox, with diminutive -ie. Other hypotheses appear unconvincing. Compare Benny (“northern or out-of-state tourist to the Jersey Shore”), or terms like touron and yuppie. The popular legend states that the term is attested from circa late 1800s, where new railroads to the Jersey Shore brought in floods of tourists to the beaches, who often carried their own lunches (rather than dined at seaside restaurants), packed by the trains in a shoebox. These tourists were then stereotyped for their habits, and the sense widened.
Etymology from Wiktionary, CC BY-SA 4.0.