Not that i'm aware of. Just update to ios 12 and be happy. Or just get your battery replaced. It's cheap. Those are your options.
id update to ios12. its faster than other software even on older devices.
I disagree with updating, at least without thinking about the ramifications.
The OP is on iOS9. Once he upgrades, he can never go back. If he has some important apps that haven't updated to 64-bit, then he'll never be able to use that app again. It would suck for the OP to lose an app/data just to update for the sake of updating.
Also, iOS9 on an iPhone 6 is blazing fast. While iOS12 is faster than iOS11, I wonder if anyone would be happy going from a blazing fast iPhone6 to whatever the iPhone6 feels like on iOS12. Can't imagine it would be anywhere near the speed as iOS9.
Lastly, to the OP. I wouldn't worry about getting a new battery at this point. If Coconut Battery's reading is accurate, you're fine. If you haven't experienced any random shutdowns, you don't really need the new battery.
However, if you do decide to take advantage of the discounted battery pricing at Apple, make sure you tell them not to update iOS, if you don't want to. They may tell you that for them to run their diagnostic, they have to update ... at which point you'll have a decision to make.
Also, there are trade-offs by not updating. Running iOS9, you run the risk of security issues that have not been patched. Only you can decide if that's worth it to update. If you're ever in the US, an iPhone on iOS9 will be pretty easy for the CIA/NSA/FBI to break into. Heck, it might be easy for hackers to break into as well if they get a hold of it physically. But what are the odds?
ft
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I was actually surprised to learn that the regular price was only $59. I enjoy servicing my own electronics so I'd likely opt for doing it myself with a $29 DIY kit if I need a new battery when the replacement promotion ends after 2018, but I don't consider $59 to have it done for me by an authorized tech to be expensive. I thought it'd be more.
The only problem with the DIY kits are that the quality of the batteries are hit/miss. I've gotten good ones for an iPhone5 from ifixit. I've gotten a good Yontex for another iPhone5. The Yontex for my iPhone6 was good for about 3 months, but it's garbage now. Thank goodness I saved my OEM battery, which I'll put back in at some point because it's better than the Yontex.