The Crossbow Expert feat (PHB, p. 165) states that you ignore the loading feature of crossbows, but does that mean you still need a free hand in order to reload it?
According to Sage Advice, yes
The article is here:
And the relevant quote is here:
What does that all mean for a hand crossbow? It means Crossbow Expert makes it possible to fire a hand crossbow more than once with a feature like Extra Attack, provided that you have enough ammunition and you have a hand free to load it for each shot.
Yes, the feat only affects loading time and allows you to improve your rate of fire through class features like Extra Attack.