Orange and Black Wire?

I'm fixing an old Conair cordless razor, battery finally died. Bought the battery and I'm ready to solder it in, but one problem. I don't know which wire is which. I'm faced with a black and an orange wire. Black is top, orange is bottom. I'm guessing that the black is positive and orange is negative? If I'm wrong though, I'm afraid I'll kill the battery if I charge it backwards. I'm not sure how a multimeter would be helpful here since there's no current, and I can't put it in the charger with the battery cover taken off and I can't use a multimeter with it in the charger. lol I only know a tiny bit about electronics, I'm a beginner at this... I've only used a multimeter once or twice, so I'm not even sure if I'd be using it correctly if I tried using it, but I'm willing to learn! Hoping someone can help me here?

 

Yeah I knew someone was going to lecture me about that. I was really out of it, some kind of stomach bug. Felt horrid but it needed to get done. After I took it out and had it in my hand... I looked at it and said, "Oh crap..."

Before I post any pictures, does the fact that they used white heat shrink on the orange wire mean that it counts as a white wire? Or does it have no significance?

 

Damn... turns out the motor is fried. Never mind. I told the owner to buy a Panasonic ER224 Wet/Dry. That's the best bargain clipper I've ever owned. I recycled the parts. Sorry I wasted your time.