Don't recycle, just replace with something cheaper.
One of the main reasons I went down the self-build route was to have complete control and freedom over the type of battery I use. As I built a folding electric bike, my priority was to make the battery as light as possible and portable to carry in a bag, should the need arise. With this requirement in mind, I purchased a small 5Ah LiFePo4 battery complete with built-in BMS and a charger. The battery measures 150x110x90mm and weighs just 1.8kg. I've found it more than capable of providing for my needs, and it only cost me £90! So cheap that I purchased two of them.
It's not difficult to do your own battery solution like I have onto a ready-made electric bike once its battery goes. Obviously you might need to change connectors, do a bit of soldering, and find a suitable carrier for the battery pack (I use a little bag on the handlebar)..but it's worth the effort as you can make a considerable and ongoing saving and avoid adding unnecessary excess weight to your bike.
If you don't feel confident enough, you could get someone who has basic electrical skills to do it for you..if you can wire a plug and use a soldering iron, you shouldn't have any problem.