I wouldn't try to wait around to have a private conversation. I would probably walk by their office and peek my head in- if someone else is in there I'd say "oh, sorry- I didn't realize someone was in here. Hey, when you have a minute could I speak with you in private?" At that point the other person would either get the hint and leave if they're not having an important conversation, or your HR person should say "yea, let me wrap this up and we can chat" or you might offer "I can come by at the end of my shift?" or something.
I would never ever ever feel awkward if I was talking to anyone in leadership and a TM came by while I was talking and asked the other person to talk in private. I would feel a little weird if that TM just hovered, essentially trying to push me out of the room so they can have their private conversation. First come, first serve, imo. If I'm already engaged in a conversation, don't try to edge me out!
If you're not worried about starting the conversation, but more worried about people dropping in while you're having the conversation, just ask your HR person if it's cool if you shut the door- that you don't really want the whole store knowing something. They'll absolutely understand- it's basically in the job description that HR will be dealing with sensitive/personal issues of the employees, so if anyone in the store will understand the importance of a closed door conversation, it'll be HR (assuming you have a remotely competent HR person, of course!)