Considering that hilts can be made out of wood, there is no reason you wouldn't be able to make a hilt out of Cortosis.
Legends:
Cortosis ore was a very rare, brittle, fibrous material whose conductive properties caused lightsabers to temporarily short out upon contact.
It would appear that a cortosis hilt, when struck by a saber, would cause the opponent's blade to short out.
To avoid your own blade shorting out, the inside of the hilt would need to be made of different material with the protective cortosis being only on the outside.
Only lightsabers that used a special kind of lightsaber crystal mined on Mestare were immune to the effects of cortosis.
A hilt made of cortosis that also uses this special crystal from Mestare would probably be even less likely to cause its own blade to short out.
Cortosis was expensive to mine because it was so rare and it had to be absolutely refined.
Since the material is rare and sometimes even dangerous (in it's pure form), it's unlikely many Jedi would seek to build their hilts from it under normal circumstances. Jedi train for lightsaber combat, so they'd simply try to train themselves to avoid leaving their hilts open to attack.