Having superior firepower is definitely the least headache-inducing way to deal with skirmishing cavalry. I normally eschew missile troops in my current (Romani) game, but in western North Africa I happily spam slingers. Numidian cavalry is just so annoying if you aren't able to mow them down with missiles.

Horse archers are obviously more dangerous, but just back your slingers up with some heavy infantry in case they get charged and you should be fine. Cavalry isn't really necessary in this situation, except to pursue any routing infantry they may have and perhaps slaughter their foot skirmishers, if your own don't deal with them.