Can you drill those new weapons and put your custom runes? While they might be slightly stronger in terms of dps, I think it would be better to use your standard equipment. And even if those new weapons had empty rune slots, I wouldn't put a single rune in them. Imagine your game crashed and you are kicked from the Chaos Vortex, thus the rented weapon disappears with your precious Hatred X, Recon VI, Curse, Raid or Wrath runes inside. Yay.
The rented weapons you can not drill or add any runes or put in the arcane transmutor at all. They come as is with 6 pre-set stats, tier 10, plus 16, a durability of 200 and no rune slots. From the info I had received about the weapon is that when you rent it, it will be in your inventory but you can't use it besides in the instance, so only equipable and is not red boxed in the item slot if in chaos vortex. But according to some sources the item has a different effect which I cannot say.