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I think its fine! Half the time people get nicknames that are nowhere near their actual name (an example being [name_m]Harold[/name_m] and literally EVERYONE called him [name_f]Babe[/name_f]. Or my grandpa’s name is [name_m]John[/name_m] but he goes by his middle name [name_u]Merle[/name_u]). I think it’s just fine! 
[name_m]Connor[/name_m] nn [name_u]Cory[/name_u] definitely works! It’s easy to see where it comes from and has the same laid-back vibe.
I think it’s quite a stretch, but a lot of nicknames are; like [name_m]Hank[/name_m] for [name_m]Henry[/name_m] or [name_m]Jack[/name_m] for [name_m]John[/name_m]. Nicknames don’t have to make sense, so I wouldn’t worry about it.
[name_u]Cory[/name_u] works great as a nickname for [name_m]Connor[/name_m]! 