Since we're talking 27 MHz, you can make a pretty nasty splice and as long as the wires aren't shorted, you will only be able to tell the difference with a network analyzer.
So, although a proper repair is always desirable, a careful splice will work fine. I'd strip each cut end about 1/2 an inch, bare each center conductor a quarter of an inch and solder them together.
Next, I'd insulate the exposed center conductor with some of the center dielectric cut approx in half and taped in place, trying to wind up with the same inner conductor/dielectric diameter as the original. But, at these frequencies, it isn't very critical.
Then I'd tin the outer conductor ends and bridge them with some more braid, 4 pieces of #20 ga solid hookup wire or similar or some solder wick.
Finally, I'd probably stiffen the repaired area with a couple strips of anything handy, like wire tie pieces or a narrow strip of PC board material, and tape neatly.
If you've soldered before, repair might take 10 minutes, then you should be good to go.