I would not think a solder joint in the antenna would affect the reception any more than all the bends and loops created when it is installed in the airplane. Just how many people have the antenna absolutely straight along its entire length? Some radio manuals I've seen recommend looping the wire thru a piece of cutoff servo horn where it exits the fuselage - that would affect the impedance as much as a solder joint would.
Personally I would rather replace the entire antenna, rather than solder it in the middle, because the solder joint creates a spot that is more likely to break. You can buy antenna wire, just cut it to the same length as the original.