At times I throw 1/4 jigs on 15lb line (mono/copoly), not really a problem on the 200 size, for me at least. Might need some practice to coax out there but you'll get good distance. Around here though we have pickerel/musky/pike problem here and I can't really say 15-20lb line stops the cut, it's more about hook placement when it comes to non steel.
I was asking about the weight size since 1/4oz is small and if I recommend using a steel leader then a larger size should help a bass focus more on the lure. At times when I fish in a toothy critter area I'll use a short (6-8in) steel leader around 30lb and cut off the snap swivel and tie directly and replace the clasp with a smaller one.