If you use decent cable then 20m is not a problem. I have run PA speakers on 50+ metres of cable before now using little more than 13A twin core mains cable. Had little real effect on sound.
Wireless speakers, in the sense of zero wires don't really exist. They still need a power supply to run the onboard amplifiers. So if there is no mains anywhere near where you want to site the speakers then you are hardly any better off.
Don't worry so much about the sound quality. The quality of the speakers themselves and the acoustics of the room are probably going to have a much more noticeable effect than a bit of wire. Unless you do something really silly and try to run them on an offcut of old telephone cable you happen to have lying around. Use something that is at least as thick as 6A mains and preferably a bit thicker and you will not have any problems.
The other bit of advice I would give is to replace the entire run from amplifier to speaker. It is not really a good idea to splice the new wire onto the end of the existing wires. If there is absolutely no alternative then use a screw connector block rather than (as I have seen) just twist the bare ends together and wrap a bit of sellotape round them!
Oh and make sure you get the +ve and -ve the right way round on both speakers. Getting one wrong will have an effect on the sound.