(On page 3 of the HV9910B datasheet it says that "Iin,max" is 5mA when Vin = 8V.
Surely this means that as long as Vin is above 8V, it can supply 5mA from its VDD pin?
Presumably, if Vin is greater than 8V, then the Vdd pin can supply more than 5mA? )
From the datasheet it looks as though you could maybe just manage it. Assuming no external FET is connected the IC internals should be drawing 1mA. Add on your 4mA load and you're right on the limit at which the IC goes into under-voltage lockdown at Vin = 8V.
Presumably, if Vin is greater than 8V, then the Vdd pin can supply more than 5mA?