'shoe-like' is a compound of English 'shoe' + the suffix '-like', where 'shoe' originally meant 'a covering for the foot' and '-like' meant 'having the form of or similar to'.

'shoe' comes from Old English 'scōh' (from Proto-Germanic *skōhaz); the suffix '-like' comes from Old English '-līc' (related to German '-lich'). The modern compound 'shoe-like' is formed by combining these elements in Modern English.

Initially the elements meant 'foot covering' and 'similar to' respectively; combined, they have consistently meant 'resembling a shoe' in modern usage.