The way that the stones seem to work is that when they are wielded, they supercharge their bearer with a huge amount of energy that (if they're not strong enough) will kill them. Thanos and the Hulk are able to contain this energy because of their nature, and Tony was able to withstand the energy because of his suit and arc reactor. That is why Quill was able to survive once his friends linked up with him, there were multiple people dispelling the energy of the power stone instead of all of it being poured into Quill. Also, the entire point of the infinity gauntlet was to help contain and control the energy of all the stones at once, if someone tried to use all six stones without the gauntlet, it would probably be suicide, even for Thanos.
That being said, we need to look for some BIONICLE characters who can contain and control great amounts of energy and won't become overloaded and consumed by it (like the Bohrok Kal).
I'd wager the Toa Nuva could handle the stones if they were able to dispel the energy into the Nuva symbols since that is what they were created for, to hold the Nuva's energies because they were too great for their bodies to hold. I'm also certain Teridax, or any Makuta could, and the energies might even make them stronger, since their essence is pure energy anyways, it might feed their strength (like antidermis does with Brutaka). Speaking of Brutaka, I'm pretty certain he and Axonn would manage, we never really were told hold strong they were, but they are pretty high up there. Going back to the Quill scenario, I'm certain that any Toa Kaita would be able to manage this as well.