Tbh, either butchers' or butchers would apply to multiple butcher's shops, in the same way that butcher's or butcher would apply to an individual butcher's shop.
"I'm off to the butcher's" and "I'm off to the butcher" are equivalent in use, and both are in common usage.
(The item possessed by the butcher - the shop - is implicit, but real. Which is why it is fine to say butcher's. You are essentially abbreviating butcher's shop down to butcher's.)
However, because butcher's - in the sense of an individual butcher's shop - is a homonym of both butchers and butchers' - in the sense of many shops each belonging to an individual - it is usually necessary to get rid of the ambiguity in conversation.
The usual use of butcher's is to refer to one individual shop. If you said "The butcher's are closed", it might easily be perceived by the listener that you mean your usual butcher's shop is closed.
You might want to say "All the butchers' are closed on Sunday" for clarity.
Because the butchers is a plural word ending in 's', the English possessive is butchers'.
For documentary support : q.v. Wikipedia - English Possessive (link) and Purdue University Online Writing Lab : The Apostrophe (link)
Sport is a singular noun ("a sport"), whereas sports is not only the plural of sport, but also by convention refers to the general category of all sports. Example: "Tennis is a sport. Tom likes sports, but Harry only likes one sport."
Regarding phrases like "sport(s?) shoes": the way it is usually spoken, you can't hear the difference anyway, so the question is a bit esoteric. BUT the "correct" version (in AmE) would be sports shoes because we are talking about the category of sports. If the shoes are intended for one sport only, then you would say the name of the sport: "baseball shoes".
Best Answer
shoe shop is the correct term in the UK, and shoe store is the correct term in the US.
Both are noun-type things made up of two words- these are called compound nouns.
You don't generally use hyphens in compound nouns unless it contains prefixes, suffixes, prepositions, conjunctions, determiners, etc, for example minimum-wage, rent-a-cop or oven-to-table-ware.
You generally only make the final word in a compound noun plural. So, even though there are many shoes in the shop, you do not make shoe plural.