One of the tactics employed by foot soldiers ...when faced with Elephants ..is to sever the trunk
A highly sensitive organ, the animal would suffer extreme pain and would be panicked and would often run away. That said, armour and chainmail was used to protect this vunerable area. The weight and restrictive movement of the armoured trunk would also make wielding a sword even less likely.
Psychological warfare perhaps, is a possible answer, that being the case, the sword would only have too look 'impressive' and not be functional. Too look impressive it had to be large, but not being functional it could be made lighter with a very thin spine to allow the elephant to hold it more easily.
Many Mughal War Elephants had chains (with heavy balls attatched) fitted to their trunks to lash out at the opposition.
"A beautiful example of chain-mail armor and an elephant trained to swing a chain-weapon in its trunk. The chains on the elephant's feet would be tightened or staked into the ground to prevent it from running away from the battle, if frightened."
Photo below has this caption...
"Maharao Durjansal of Kotah on His Elephant Ranasangar" circa 1760,