1+ Need a low current charger.
A Micro Lipo or LipoNano is an easy option (100mA). Modding a tp4056 charger board would be the least expensive option.
With a tp4056 board a 5.1k resistor gives 250mA, 10k for 130mA. A through hole resistor works or a 0805 resistor. The original resistor is 0603 but 0805 did fit on the pads. FT $1.56 0805 3.9K-62K Resistor pack 270-Piece