Just for clarification, you are talking about 40 mAh NiMH button cells? If so, trickle charge current of 1.1 mA seems appropriate. Standby current is however hardly 40 mA, do you mean 40 µA?
The circuit looks basically O.K., but the capacitor is unnecessarily large, sourcing about 35 mA DC. Can be reduced to 0.15 or 0.22 µF. Or even lower with slightly reduced LED current.
NiMH lifetime can be probably increased with lower trickle charge current, e.g. 0.5 mA.