Old bluetooth speeker battery

Hi I purchased this speaker whilst on holiday 7 ish years ago. It has little to no value but i hate throwing things. The battery doesnt hold a charge. I have found a 3.7v lithium battery same dimensions at £6.

The original has no markings so i cant determin battery technology. Its charged via any usb charger does/would it be an issue if the replacement battery technology is different?

If I hookup a 3.7v lithium battery to a system that didn't previously have a lithium battery would it be sufficiently protected?

Thanks