Chosen Solution

I am about to replace my lightning connecter, but before I could switch off my iPhone, it died meaning it still hasn’t been properly shut down and is awaiting a charge which I’m unable to do, so my question is if its okay to remove the battery if the device hasn’t been shut down?

Yeah. You’re good. Use something non magnetic to disconnect the cables. Sometimes I use my fingernails, sometimes I use these Spudger You should have one of those blue/green plastic pry tools if you bought the part