A few low current chargers for 10440s: XTAR XP1 (250mA), Micro Lipo mcp73831 (100mA / 500mA, default 100mA), LipoNano (100mA / 500mA, default 500mA). Lipo nano / mcp73831 test. You can even connect an AAA battery holder to the micro lipo without soldering (twist & tape).
Modding a $1.50 tp4056 charger board would be the least expensive option. A 5.1k resistor gives 250mA, 10k for 130mA. A through hole resistor works or a 0805 resistor. Original resistor is 0603 but 0805 does fit on the pads. FT $1.56 0805 3.9K-62K Resistor pack 270-Piece
With efest10440 250mA is 0.81C, 150mA is 0.49C. LiMn might be able to tolerate more but don’t want to risk losing any capacity from charging too quick.