Two that I can find
But we are digging pretty deep into Expanded Universe territory, canon-wise.
There was Thon:
Thon was a secretive and often reclusive male Tchuukthai Jedi Master who lived in the period surrounding the events of the Great Sith War. He kept the details concerning his race, homeworld, and origins a closely guarded secret, and possessed extensive knowledge of the Force even in as-yet-unknown techniques.
He carried a lightsaber, in fact it was pretty much the only thing he did carry routinely - but did not routinely use it:
He told his new apprentice that she would use her Adegan crystals to build a lightsaber, though Sunrider was reluctant to ever use such a weapon again; she had only killed with Andur's saber hesitantly, and was disinclined to do so again. Thon explained that her previous experience with the weapon had been in self-defense, and that she had already shown great skill with the blade. The red-haired Human persisted, noting that Thon did not use a lightsaber, and that she would only accept his tutelage on the condition that she did not have to use a lightsaber.
Then there is the Unidentified Tree-Like Jedi:
A female treelike Jedi was a member of Luke Skywalker's Jedi Praxeum on Yavin 4 by 23 ABY. Despite being able to move at a slow pace, she would often stand still in the sunlight, contemplating the Force and her place in the universe.
Again, she could use a lightsaber, but generally did not:
Despite her plant-like nature, this Jedi was capable of using a lightsaber. She would hold the knobby weapon in a curled, handlike appendage. However, members of her species did not have enough stamina to engage in real duels, since the mere act of using the saber to cut through a tree trunk would drain them from their energy.
She found other means:
During the Second Imperium Crisis, the treelike Jedi was tasked with protecting the academy from potential invaders. She once stopped two Dark Jedi intruders from the Shadow Academy by crashing a dying Massassi tree trunk on them. However, this single feat had drained many months of her energy reserves, and it took a long time to recover from this intervention.
So yes, but expect to go off the beaten path in terms of Jedi to find them. As Obi-Wan said, the lightsaber is an elegant weapon and pretty much stock and staple for the Jedi.
And no, I am not about to count Skippy the Jedi Droid.