Like Kevin Reid says, you could be fine without a balun, especially at a mountain cabin where there there may be nothing to generate noise. For a receiving application, proper attention to the feed arrangement keeps the feedline from becoming part of the antenna, and since the feedline is usually near computers, switch-mode power supplies, and other sources of noise inside, this can be a huge improvement. However if there's no electricity besides a battery and your radio at the cabin, then none of these noise sources won't be around.
But if you did want to make a balun, there are options that don't require any sort of ferrite core. Many depend on a quarter-wavelength transmission line, but you want a broadband antenna so let's exclude those.
One option is a folded dipole.
simulate this circuit – Schematic created using CircuitLab
Sometimes folded dipoles are made from ladder line since it provides two parallel conductors. The two conductors are shorted at the ends, and one of the conductors is cut in the middle to make the feedpoint, labeled A and B. It could then feed like an ordinary dipole, either with a balanced feedline, or with coax and a balun.
But notice the center of the other wire is ground: the voltages on the left and right are always equal but opposite, just what you want from a coax shield. If you could somehow connect the shield there, but then also connect to the feedpoint on the other side...
Solution: build the folded dipole from metal tubing, with a tee at the ground point where the feedline can enter, then pass inside the antenna to the feedpoint on the other side. If 10 meters of tubing isn't what you had in mind, then just use coax, which is already a tube!
The connections you need to make for such a construction are drawn in blue. Note that it's the shields of the coax that make the folded dipole, while the feedline runs inside the left half of the antenna to connect at the feedpoint at the top. The center conductor on the right half does nothing: cut it off and ensure it can't come in contact with the other parts.