Presumably it is the 12volt fittings in your caravan you are replacing. The "Ballast" in these isn't a ballast at all but is an invertor increasing the 12volt supply to around 90volts at a fairly high frequency to strike up the original conventional fluorescent tube. Yes, it must be wired out or would destroy your LED lamp.
The fitting will almost certainly only have one connection to each tube end. The heaters are not used in 12volt invertor systems. That's why the tubes quickly darken at the ends.
The LED "tube" you have bought is presumably designed specifically to retrofit into caravan/boat fixtures, so will surely expect one connection to each end. It would be very difficult to have to rewire the holder in a miniature fitting.
You won't hurt a 12 volt LED lamp by reversing it's supply, (at rated voltage of course). It's a group of diodes and simply won't conduct. Forward biased LEDs emit light.
When I converted my caravan lights I bought LED strip, which you can cut to length, and was much cheaper than conversion tubes. Not much difference in the work to install it, as you have to rewire the fitting anyway.
ps Checking diodes with a multimeter can be confusing. Apart from the forward volt drop of the diode giving strange resistance readings, it's the black probe of the meter which is connected to the +ve of the internal battery.