Thank you! Sorry my response wasn't usable.
In camera with a white background? I don't think it is possible. Still, here are three other options that might be worth trying, and one suggestion.
1. Fast lens, wide open, ND/VND filter. Get everything on the front of the bottle in focus, and you'll make the back side of the bottle - the label on the bourbon and the text on the moonshine - go out of focus. They'll still be there, but maybe not as prominent.
2. Angle the bottle 45° and shoot that way. While you'll get some of the back things in focus, you'll be able to see the things properly on the front. If you have a tilt-shift/perspective correction lens, all the better! You can "tilt" and keep the front in focus and the back out of focus, at least a little.
3. Shoot with a white background, and do what the client wants, to the best of what is possible. Then, do a shot with the black background on your time. Make it as good as you can. If it looks great, show your client what is possible. If he likes it, great. If not, then he's lost nothing. If it would really be a Bad Thing to do, don't bother. An unhappy client with a photo he wanted is far better than an angry client with a photo he didn't want.
Your client isn't a photographer. That's not his job. Part of our job as photographers however is to educate. With a white background, anything on the back of bottles such as those is going to be visible if you're working 100% in camera. There's no way around it. Take the moonshine. It's a clear liquid in a clear bottle with black printing on both sides. With the lighting you need and the white background he requires, all of that printing is going to be visible. There is no way around that. You will see the printing on the backside of the bottle. Your client needs to understand that. I get that he sells bottles that are rare in Australia, and wants to show exactly what is for sale. There's actually a bit of extra credibility in having the label on the back of the bourbon and the text on the back of the moonshine.
"Look at this, Mate! This is the same bottle from the website. It's got that label on the backside."
"Probably fake, Mate."
"No, no. I saved the picture. Look!"
Your client is going for authenticity. There it is. It's the bottles with the label, the printing on the back, the imperfections that could be corrected in Photoshop if only we had the time.
Hope this helps. Good luck!