Your assumptions re both chargers & solar controllers seems incorrect.
It seems likely that a properly designed mains input battery charger will meet your need.
I'll assume you are using a lead acid battery - although similar statements apply to eg LiIon batteries.
Essentially all equipment intended to charge lead acid batteries will only take such input energy as required to charge the battery at any stage during charging and once fully charged. During charging low cost PWM controllers will usually supply whatever current the source will supply when directly connected to the battery and MPPT controllers will attempt to maximise power transfer from the source. In other than very low controllers, cost current is usually able to be limited to a preset maximum (which is chosen based on battery specifications).
Lower cost mains chargers tend to supply whatever the battery will take within their capabilty.
Chargers or controllers of more than basic spec will provide a "boost charge" at the end of the charging cycle.
However, once charged either device will float the battery and use only such energy as is required by the battery in 'float' mode plus whatever standby current the charger requires. (LiIon batteries are not usually "floated" - charging is terminated when complete. (Floating at lower than full voltage is permissible but this is not usually done.))
No "proper" battery chargers or solar controllers consume high levels of energy once the battery is charged.
Controllers designed for wind turbine use will divert the input to a "dump load" once the battery is charged due to the need to not allow a wind turbine to operate unloaded.