What ever you do, do not put a rechargeable Lithium Ion cell in your Amiga, you could set it on fire!
Li Ion cells require close control when recharging, over do it and they explode! All current Li Ion charging systems including mobiles have dedicated charging chips.
You can get Lithium cell batteries that are coin shaped and have a long life. To use one of these you would need to remove the connection from the Amiga's charging circuit, typically a 1N914 diode.
You can safely replace a NiCad with a NiMh cell and leave the charging circuitry intact. NiMh cells do not have the corrosive 'goo' of NiCads.
