Dual-wielding climbing axes eh... wonder if lara learns some martial arts to take advantage of that for close-combat.
And.... Not that they'll do it, but I just had the idea of upgrading those to something like tonfas (ala Ninja Gaiden II). Not sure if that'd be better for climbing though, single spike vs entire length of spikes, though I was thinking the orientation of the handle would be less stress on the hand grip (climbing like you're crawling horizontally). It'd also be something like when Bruce and Ra's were sliding down the mountain in Batman Begins, and Bruce uses his forearm guard spikes to stop from falling off.
Maybe that's too hardcore for Lara. Giant spikes on her forearm for climbing/melee while dual wielding desert eagles. ahem.