‘Go and put your shoes on’ is correct British English. We consider ‘Go put your shoes on’ as incorrect grammar. So ‘try and put your shoes on’ would also be natural. I’m trying to think what other verbs this would work with because ‘find and put your shoes on’ doesn’t sound right in British English but neither does ‘find put your shoes on’ in US English perhaps someone who understands grammar better can explain why some verbs work with this construction and some don’t.