OP, I think the confusion is that you are using the term "hilt" in its normal meaning, when for crew skill purposes it means something else.
Hilts made by artificers can be slotted into ANY lightsaber type: single or double-bladed. However, the lightsaber in question must be able to be modified. You will know if a lightsaber (or any item) can be modified because when you look at its stats it will look something like this:
Hilt <----- This is the piece that Artificers make
It will also NORMALLY be orange or purple colored, but companions often have green lightsabers that are fully customizable.
For double bladed lightsabers, those are used by Shadows/Assassins and the needed stats are Willpower and Endurance. The hits that those users need are called Resolve Hilt (X) or Force Wielder (X). You can start making hilts as others have said in the tweens.
* - Artificers also make enhancers but you didn't ask about those.
What colour Lightsaber crystal can I make first I have the yellow founder one but I'm still quite new to swtor?