Correct charging current for lithium-ion batteries
CC/CV charging means that it begins by providing a constant current until the voltage hits a preset level, then switches to that constant voltage until the current trickles down to something marginal.

The internal resistance of the battery doesn't affect the charging routine, although the charging efficiency might change.

This target charge current is relative to the battery capacity ("C"). For standard Li-ion or Li-polymer batteries, chargers often target 0.5C charge current. In other words, if the battery is rated at 500 mA-h, the target current is 250 mA.

It is not unusual to charge at 1C (500mA), but this compromises the battery's capacity over time.

I don't know about Synergy's "Advanced Hybrid" technology, but the voltages match standard Li-Po batteries. I would choose a new battery of (at least) the same capacity.

Hopefully you can find one that fits! Obviously, if you have to reduce the capacity to reduce physical size you risk charging the new battery too fast.