RG6 coax, if quality line is used, will work just fine for the quarter-wave matching stub. RG6 coax is used by many for feeding the four verticals of four square antenna systems on 160-20 meters.
You just have to be very careful that you use high quality line with a good shield. Some of the imported line has very little wire in the outer shield.
I would use RG6 Quad and make sure that the center conductor is 18 guage and not some of the thinner center conductor cable you sometimes find. and if you are lucky, you might even find some RG6 that has copper braid.
Good quality compression connectors like Thomas and Betts or commercial RG6 crimp connectors will work. Personally I have just used PL259 connectors with reducers on most of my low band receiving antennas. You can't solder the aluminum sield but you can create a good tight fit into the connector.
Also sometimes you can get CATV flexible RG-11 at very low cost or even free. This larger diameter 75 ohm cable is used for long runs from the street to the house. It will easily handle 1 KW plus.
73 Dennis W0JX