EvanNave55
Explorer
I would say you can without fault thanks to the errata of the PH
"Two-Handed (p. 147).
This property
is relevant only when you attack with the
weapon, not when you simply hold it"
As we can see you can hold the weapon in one hand, except when attacking. If you do a S spell attack you do have one hand free thanks to the errata. There is no need to take War Caster just to enable you to cast S spells, but the other buffs it gives you makes it worth taking.
We aren't discussing casting spells with a two-handed weapon, we're discussing casting spells with two separate weapons.