If the trailer has brakes then you MAY NOT TOW IT without a properly charged battery in place, this is a safety issue, and a liability issue, the reason is that said battery is part of the emergency (Break-a-way) Braking system and without it you have no emergency braking system, period.
As for plugging in: SOME converters, most notabilly the old Magneteck 6300 line, really do not like operation without either a battery or a battery simulator. Now sometimes they work, but I'd not count on it.
That is the bad news
now the good news.
I have one of those handy-dandy jump start devices,, I have had to use it many times over the years for assorted vehicles (not all mine) (Worked for a time for a tow company, many owners coming to redeem their impound needed a jump) .
I'm on my 3rd unit now... This is battery enough for the job, Set it in the battery box hook it up and you are good to tow.
IF you have one of those old magnetek converters.. May I suggest a Progressive Dynamics 4600 line from Best converters.
Replacing the guts of the Magnetek with the PDI woudl be like upgrading from a skate board to a Cadillac it is true, (Worst to best) but hey... That is why I recommend it)
Home is where I park it!