My Drapion has a bunch of EVs in defense, although I don't remember exactly how many. It was probably something like 252 speed, 160 attack, 96 HP. This means it can usually take a hit or two in order to put down toxic spikes and then attack. My strategy was to rely on Sniper, with high-crit moves and razor claw, although in practice it doesn't work quite as well as I hoped.
Move-wise you are right, Cross Poison doesn't really cover a lot of ground, but it also has a high critical hit ratio and is good for Fighting and Dark types, which resist Night Slash. Plus you get super-effective on grass.
My fourth move was Brick Break which I thought at the time covered more ground, but TBH Earthquake is probably a better move. Maybe you could try Night Slash, Earthquake, Brick Break, Toxic Spikes?
If you don't want to invest EVs in defenses it may be better to switch TS out for Swords Dance like you said and use Drapion as an outright physical sweeper.