Fighting melee as a warlock is like trying to kill somebody with ranged weapons as a rogue/warrior.
It is hard, way too long and probably a very dumb thing to do in almost any situation.
As a warlock or caster of any kind you are looking for weapons with stats, not with melee damage so you won't be looking into procs. And firestone is not much of a great thing, I wouldn't invest points into improving it if they paid me.
A good wand will cause a lot more damage than a melee weapon any day, against just about anything and everything. It doesn't have a minimum range and doesn't use ammo, what more do you want ?
Seriously, the only time when you would even consider using melee rather than wanding away would be when you have no wand equipped due to using a Spellstone in its place.
Alas, you are free to do whatever you prefer I have done my part by warning you :P
PS: Slower weapons always have a higher proc rate, and yes, firestone will cause higher damage by hit with a slower weapon.