Is a decent hexcrossbow warlock possible?

Hex warrior lets you use charisma on an attack role, and improvised pact weapon lets you have a light crossbow or heavy crossbow as your pact weapon. However, Hex warrior specifies that it has to be a weapon without the two-handed property, which means it can't work with a light or heavy crossbow, but improvised pact weapon doesn't work with hand crossbows.

It seems like crossbow hexblade warlock is too unsynergetic and everything is working against it, do any of you know of a way to make this work?