One fun trick with learning Welsh is I have to translate from Canadian English to British English before then crossing over to Welsh. "Trainers", as a term for shoes, is completely unknown in my idiolect.
You'd be more likely to say 'Sneakers' wouldn't you?
In my idiolect, "running shoes" is the standard term. There may be areas of Canada where "sneakers" is standard, but I associate the term with American English.
‘Running shoes’ is also the standard term in Australia. As you say, ‘sneakers’ sounds American and ‘trainers’ sounds British.