As an electronic engineer, permit me to comment.
An appliance that uses, say 120 watts, will need a supply capable of supplying more than that - to give some head-room; say 50% above, so a supply of close to 200 watts is what I would recommend in a 120 watt example. A car battery charger will probably not be suitable as it will only deliver a few amps (120 watts is 10 amps at 12 volts) in most cases and it is also expecting to have a battery on the end of it which will stabilize the voltage in the way that a heating element won't. Even if it can deliver the current, it might not work as expected or safety circuitry inside might shut it down if it is expected to do something it's not designed for.
A car 'fast-starter' thing if mains powered will also not necesarily work either as it is expecting a car battery to be on the end of it and the output voltage of the fast-starter could be way-off (too high) if not connected to one - or safety circuits could shut it down as the 'load' we are putting on it is not as expected. A battery powered fast/emergency starter usually has a sealed lead acid battery inside and could work; see paragraph below, next but one. (I use a 4Ah battery from an emergency car starter device). No need for mains in this case.
In addition we need to conder dragging a mains electricity cable around the apiary for any mains powered device. Do-able but perhaps not desireable. Note that an electric hedge trimmer is 'double'insulated' and designed for outside use.
It may not be necessary to lug around a full-sized car battery; most smaller sealed lead-acid ones from Yuasa and others will work although some are not designed for high current discharges so the specifications need to be checked. However, if you were to need to treat a large number of hives, a small battery might not last the distance. Example :- Using a 120 watt heating element, it will draw 10 amps from a 12 volt battery. A 10 Ah battery will last 10 amps for 1 hour. A 2 Ah sealed lead acid battery will therfore last 1/5th of an hour - 12 minutes maximum. Again, you would need to have some 'head-room' as any drawn current from the heater may be higher than specified and batteries don't work so well when cold.
May your bees read the same books as you do.