Doesn't look like it charges to 4.35v just 4.2v.
So you could use it with a 4.35v but you won't get full capacity of the battery.
Details:
Charges and provides extra backup power to all devices that supports USB charging. E.g. iPhone, Android, tablets, MP3 players, GPS units, etc
Carry multiple batteries with you to get virtually unlimited backup power on the go
Charge port on-board -- charge up your backup batteries from an USB port without carrying a separate charger
850-900mA charging current
Over-charge (4.2V) and over-discharge (2.9V) protection, reverse polarity connection
Single TP4056 IC for battery charging
Single PT1301 IC for charging devices
PC-ABS flame retardant material
1200mA typical output (new in Miller ML-102 v5, currently shipping)
http://i.imgur.com/fKSQtVA.jpg..........You self made victims crack me up. =D