How to replace the internal battery?

After poking around the dark corners of the internet, I think I have enough information for you to accomplish your battery replacement. The first place I'd start with is the iFixit guide for the QC 35; after close examination it appears the process is identical for your QC 35 II, so this guide will get you there.

Bose QuietComfort 35 Battery Replacement - iFixit Repair Guide

Just to be safe, you can check out the QC 35 II audio jack replacement guide that'll show you exactly how to get the earpiece open; I didn't see any differences, but I mention this just to cover all the bases.

Bose QuietComfort 35 II (Model 789564‑0010) Audio Jack Replacement - iFixit Repair Guide

One guy on Reddit also had suggestions on how to do that same replacement on your headphones, so it might be worth your time to take a look at what he had to say about it, and he added pictures as well.

Replaced battery of bose qc35ii after 4 years : r/bose

Finally, another guy posted a YouTube video of the whole process on a QC 35, but again it seems to be the same for those and the QC 45 models as well.

Replace Old Battery on Bose Headphones – Easy at Home! - YouTube

As far as parts go, the 35, 35 II and 45 all take the same battery, so you won't have any trouble getting a replacement; in fact, you can even buy one right here on iFixit if you want to support their repair efforts.

Bose QuietComfort 35 Battery

Of course, for the cost conscious there are several alternatives as well; I found sources on Amazon, AliExpress and eBay that would all work.

As you work, take lots of pictures and once you're done you can use them to create your own iFixit guide to your battery replacement. It's easy, fun and will earn you the respect of the repair community.

Create a new Guide - iFixit

Good luck, and let us know how it all turns out!